One Hat Cyber Team
Your IP :
216.73.216.115
Server IP :
194.44.31.54
Server :
Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64
Server Software :
Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k
PHP Version :
5.6.40
Buat File
|
Buat Folder
Eksekusi
Dir :
~
/
home
/
vo
/
book-newprint
/
Edit File:
the.aux
\relax \@writefile{toc}{\contentsline {section}{Preface}{{\reset@font 4}}} \citation{34} \citation{32} \citation{31} \citation{33} \citation{121} \citation{olsh} \citation{76} \citation{cur_re} \citation{aus} \citation{gab_roi_book} \citation{shmr} \citation{sh_kol_etal} \citation{sin} \citation{akh_glaz} \citation{halm2} \citation{reedsim} \citation{137} \citation{69} \citation{ber_us_sh} \citation{kiril} \citation{zhel} \citation{59} \citation{78} \citation{26} \citation{douglas} \citation{arv76} \citation{take79} \citation{28} \citation{kad_rin} \citation{118} \citation{murphy} \citation{34} \citation{jor_moore} \citation{book} \citation{jorg_book} \citation{135} \citation{kac} \citation{lus} \citation{rief_book} \citation{chari} \citation{mad1} \citation{jant} \citation{klim_sch} \citation{kor_soi} \citation{7} \citation{70} \citation{sak} \citation{wielandt} \citation{conn} \citation{manin2} \citation{holevo} \citation{partas} \citation{boz_sp91} \citation{142} \citation{116} \citation{halm2} \citation{ern} \citation{murphy} \citation{abdes} \citation{adjan_book} \citation{akhi_book} \citation{akh_glaz} \citation{araki60} \citation{54} \citation{arz_ver2} \citation{arv89} \citation{azi_io} \citation{90} \citation{barn} \citation{benk_ii} \citation{65} \citation{68} \citation{black} \citation{boz_sp91} \citation{102} \citation{cuntz} \citation{dal} \citation{73} \citation{111} \citation{quesne3} \citation{quesne} \citation{dyk_nica} \citation{gab_roi_book} \citation{gelpon} \citation{gli} \citation{goldin} \citation{gol} \citation{19} \citation{heb_etal} \citation{inoue} \citation{isma} \citation{jones89} \citation{jorg_book} \citation{jor_moore} \citation{jorg_s_w} \citation{jorg_wer} \citation{kiril2} \citation{koe} \citation{koor_sw} \citation{krugl_q} \citation{kru_r_s} \citation{kul} \citation{17} \citation{20} \citation{mis} \citation{murneu} \citation{nagy_nica2} \citation{nelson} \citation{niz_tur} \citation{olsh} \citation{lomi} \citation{umz95} \citation{non} \citation{ped} \citation{pow_i} \citation{pow} \citation{proskurin} \citation{pro_mfat} \citation{pro} \citation{pusz_anti} \citation{pw} \citation{36} \citation{rab_mfat} \citation{135} \citation{133} \citation{132} \citation{134} \citation{shwe_we} \citation{82} \citation{81} \citation{silv} \citation{sklyan} \citation{skl_2} \citation{138} \citation{take79} \citation{tam} \citation{11} \citation{thoma} \citation{144} \citation{130} \citation{vas} \citation{vasil} \citation{voi_dy_ni} \citation{wen} \citation{103} \citation{wor87} \citation{wor_aff_2} \citation{zachos} \citation{zhe} \citation{flato} \citation{goodman} \citation{kad_rin} \citation{renau} \citation{vasi} \citation{yama} \citation{zak} \citation{kaz} \@writefile{toc}{\contentsline {chapter}{\numberline {1}Pairs of self-adjoint operators connected by quadratic relations and some generalizations}{{\reset@font 8}}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {1.1}Introduction to representations of $*$-algebras}{{\reset@font 8}}} \newlabel{sec:1.1}{{1.1}{{\reset@font 8}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}$*$-Representations: key words}{{\reset@font 8}}} \newlabel{sec:1.1.1}{{1.1.1}{{\reset@font 8}}} \newlabel{intertwine}{{1.1}{{\reset@font 9}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.2}$C^*$-representable $*$-algebras}{{\reset@font 12}}} \newlabel{sec:1.1.2}{{1.1.2}{{\reset@font 12}}} \newlabel{prop:cstar}{{5}{{\reset@font 13}}} \citation{wich} \citation{dor_bel} \citation{29} \citation{21} \citation{30} \citation{77} \newlabel{rem:resid}{{3}{{\reset@font 16}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.3}Enveloping $*$-algebras and $C^*$-algebras}{{\reset@font 16}}} \newlabel{sec:1.1.3}{{1.1.3}{{\reset@font 16}}} \citation{117} \citation{114} \citation{115} \newlabel{ex:proj}{{3}{{\reset@font 18}}} \citation{kru_wor} \citation{15} \citation{13} \newlabel{WSW}{{2}{{\reset@font 20}}} \newlabel{env}{{1}{{\reset@font 20}}} \citation{16} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.4}$*$-Representations of generators and relations}{{\reset@font 22}}} \newlabel{sec:1.1.4}{{1.1.4}{{\reset@font 22}}} \newlabel{just_relations}{{1.4}{{\reset@font 22}}} \newlabel{self_relation}{{1.5}{{\reset@font 22}}} \citation{reedsim} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.5}Pairs of self-adjoint operators satisfying quad\discretionary {-}{}{}ratic relations}{{\reset@font 25}}} \newlabel{sec:1.1.5}{{1.1.5}{{\reset@font 25}}} \newlabel{oneone}{{1.1.5}{{\reset@font 25}}} \newlabel{onetwo}{{1.7}{{\reset@font 25}}} \citation{126} \@writefile{toc}{\contentsline {section}{\numberline {1.2}$F_n$-algebras and their representations}{{\reset@font 28}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}About $*$-representations of ${F}_n$-algebras}{{\reset@font 28}}} \newlabel{sec:1.2.1}{{1.2.1}{{\reset@font 28}}} \newlabel{th:r.f}{{2}{{\reset@font 28}}} \citation{142} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}Examples of ${F}_n$-algebras generated by idempotents and their representations}{{\reset@font 30}}} \newlabel{sec:1.2.2}{{1.2.2}{{\reset@font 30}}} \citation{naz} \citation{127} \citation{121} \citation{bon_dr} \citation{124} \citation{125} \citation{119} \newlabel{th:q2}{{3}{{\reset@font 36}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.3}Non-commutative ``circle'', ``pair of intersecting li\discretionary {-}{}{}nes'' and ``hyperbola''. More examples of $F_4$-alge\discretionary {-}{}{}bras}{{\reset@font 40}}} \newlabel{sec:1.2.3}{{1.2.3}{{\reset@font 40}}} \citation{fa} \citation{fa} \citation{rab_sam_fa} \citation{rab_sam_fa} \citation{bart} \@writefile{toc}{\contentsline {section}{\numberline {1.3}Representations of two-dimensional Lie algebras, their nonlinear transformations, and semilinear relations}{{\reset@font 43}}} \newlabel{sec:1.3}{{1.3}{{\reset@font 43}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Representations of two-dimensional real Lie algebras and their nonlinear transformations by bounded operators}{{\reset@font 43}}} \newlabel{sec:1.3.1}{{1.3.1}{{\reset@font 43}}} \newlabel{deformedlie}{{1.8}{{\reset@font 43}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Pairs of operators connected by semilinear relations}{{\reset@font 45}}} \newlabel{sec:1.3.2}{{1.3.2}{{\reset@font 45}}} \citation{sam_tur_sh} \newlabel{sr}{{1.9}{{\reset@font 46}}} \newlabel{hom}{{1.10}{{\reset@font 46}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Kleinecke--Shirokov type theorems}{{\reset@font 49}}} \newlabel{sec:1.3.3}{{1.3.3}{{\reset@font 49}}} \newlabel{pr1}{{19}{{\reset@font 49}}} \newlabel{def1}{{3}{{\reset@font 50}}} \newlabel{th1-semi}{{6}{{\reset@font 50}}} \citation{137} \newlabel{th2-semi}{{7}{{\reset@font 51}}} \newlabel{p20'}{{1.11}{{\reset@font 51}}} \newlabel{p20}{{1.12}{{\reset@font 51}}} \newlabel{l1}{{5}{{\reset@font 52}}} \newlabel{l2}{{6}{{\reset@font 53}}} \newlabel{cth2}{{8}{{\reset@font 53}}} \newlabel{p21}{{1.14}{{\reset@font 53}}} \newlabel{p22}{{1.15}{{\reset@font 54}}} \citation{143} \newlabel{c1}{{9}{{\reset@font 55}}} \citation{137} \citation{143} \newlabel{c2}{{10}{{\reset@font 56}}} \newlabel{gr}{{11}{{\reset@font 56}}} \newlabel{c4}{{1}{{\reset@font 57}}} \newlabel{ex}{{7}{{\reset@font 57}}} \newlabel{prp}{{1.17}{{\reset@font 58}}} \newlabel{mul}{{1.18}{{\reset@font 59}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Irreducible representations of semilinear relations}{{\reset@font 61}}} \newlabel{sec:1.3.4}{{1.3.4}{{\reset@font 61}}} \newlabel{connec}{{20}{{\reset@font 61}}} \newlabel{pr4}{{22}{{\reset@font 63}}} \newlabel{therg}{{23}{{\reset@font 63}}} \newlabel{mk}{{1.19}{{\reset@font 64}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.5}Representations of semilinear ${F}_4$-relations}{{\reset@font 66}}} \newlabel{sec:1.3.5}{{1.3.5}{{\reset@font 66}}} \@writefile{toc}{\contentsline {section}{\numberline {1.4}Representations of $q$-relations}{{\reset@font 68}}} \newlabel{sec:1.4}{{1.4}{{\reset@font 68}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Finitely-dimensional representations of $q$-rela\discretionary {-}{}{}tions}{{\reset@font 68}}} \newlabel{sec:1.4.1}{{1.4.1}{{\reset@font 68}}} \newlabel{prop:ssh}{{25}{{\reset@font 69}}} \citation{sam_sh_umz} \newlabel{prop:ssh1}{{26}{{\reset@font 70}}} \newlabel{skew1}{{1.20}{{\reset@font 70}}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}Hermitian $q$-plane and $q$-CCR}{{\reset@font 71}}} \newlabel{sec:1.4.2}{{1.4.2}{{\reset@font 71}}} \newlabel{q-plane}{{1.21}{{\reset@font 71}}} \citation{adv} \citation{ber0} \newlabel{q-plane_ii}{{1.22}{{\reset@font 72}}} \newlabel{alpha-ccr}{{1.23}{{\reset@font 72}}} \newlabel{alpha-ccr2}{{1.24}{{\reset@font 73}}} \newlabel{q-ccr}{{1.25}{{\reset@font 73}}} \newlabel{ds-qccr}{{1.26}{{\reset@font 73}}} \citation{ber0} \citation{bukl2} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.3}Real quantum plane and real quantum hyperboloid}{{\reset@font 76}}} \newlabel{sec:1.4.3}{{1.4.3}{{\reset@font 76}}} \citation{adv} \citation{slie} \newlabel{hyperb}{{1.27}{{\reset@font 77}}} \newlabel{hyperb1}{{1.28}{{\reset@font 77}}} \citation{goh_etal} \citation{azi_io} \citation{goh_rei} \citation{serg90} \citation{serg92} \citation{rodm2} \citation{kis_sh} \citation{10} \citation{wich} \citation{dor_bel} \citation{29} \citation{21} \citation{30} \citation{77} \citation{78} \citation{118} \citation{114} \citation{115} \@writefile{toc}{\contentsline {section}{Comments to Chapter 1}{{\reset@font 78}}} \citation{56} \citation{13} \citation{15} \citation{pop_mfat} \citation{akh_glaz} \citation{137} \citation{reedsim} \citation{69} \citation{ber_us_sh} \citation{serg84} \citation{shapiro} \citation{69} \citation{ber_us_sh} \citation{wielandt} \citation{halm2} \citation{reedsim} \citation{ver} \citation{adv} \citation{romp2} \citation{newt} \citation{smst} \citation{31} \citation{33} \citation{142} \citation{rab_sam_mfat} \citation{rab_sam_ieot} \citation{yzette} \citation{naz} \citation{127} \citation{110} \citation{ped2} \citation{halm1} \citation{116} \citation{112} \citation{113} \citation{pop_mfat} \citation{mackey} \citation{bon_dr} \citation{124} \citation{finck} \citation{125} \citation{rab_sam_mfat} \citation{rab_sam_ieot} \citation{romp2} \citation{adv} \citation{besp_umz} \citation{gal_mfat} \citation{besp_umz} \citation{gal_mfat} \citation{gal_mur} \citation{shirokov} \citation{kleinecke} \citation{halm2} \citation{bss} \citation{sam_tur_sh} \citation{sam_sh_umz} \citation{ver} \citation{adv} \citation{biede} \citation{macf} \citation{klim_sch} \citation{lomi} \citation{adv} \citation{koor_sw} \citation{adv} \citation{bukl2} \citation{heb_etal} \citation{romp2} \citation{lomi} \citation{adv} \citation{halm2} \citation{137} \citation{133} \citation{132} \@writefile{toc}{\contentsline {chapter}{\numberline {2}Representations of dynamical $*$-algebras}{{\reset@font 82}}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {2.1}Operator relations and one-dimensional dynamical\penalty -\@M systems}{{\reset@font 82}}} \newlabel{sec:2.1}{{2.1}{{\reset@font 82}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}Operator relations connected with one-dimen\discretionary {-}{}{}sional dynamical systems}{{\reset@font 82}}} \newlabel{sec:2.1.1}{{2.1.1}{{\reset@font 82}}} \newlabel{xx}{{2.1}{{\reset@font 82}}} \citation{klles} \newlabel{rel:quadratic}{{2.2}{{\reset@font 83}}} \newlabel{rel:parabola}{{2.3}{{\reset@font 83}}} \newlabel{ucu}{{2.4}{{\reset@font 84}}} \newlabel{cu}{{2.5}{{\reset@font 84}}} \newlabel{xx_fun}{{2.6}{{\reset@font 84}}} \newlabel{xx_n}{{2.7}{{\reset@font 84}}} \newlabel{cu-props}{{28}{{\reset@font 84}}} \newlabel{xx-center}{{29}{{\reset@font 85}}} \newlabel{toeigen}{{30}{{\reset@font 87}}} \newlabel{rel:chains}{{2.8}{{\reset@font 87}}} \citation{vai_fed} \newlabel{th:per}{{15}{{\reset@font 90}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}Finite-dimensional representations}{{\reset@font 90}}} \newlabel{sec:2.1.2}{{2.1.2}{{\reset@font 90}}} \newlabel{fin_th}{{16}{{\reset@font 90}}} \newlabel{one5}{{2.9}{{\reset@font 91}}} \citation{shmr} \newlabel{moebius-rel}{{12}{{\reset@font 94}}} \citation{83} \newlabel{moebius-map}{{2.12}{{\reset@font 95}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.3}Infinite-dimensional representations}{{\reset@font 95}}} \newlabel{sec:2.1.3}{{2.1.3}{{\reset@font 95}}} \newlabel{thiso-x}{{18}{{\reset@font 96}}} \newlabel{iso2-x}{{2.13}{{\reset@font 97}}} \newlabel{thirr-x}{{19}{{\reset@font 97}}} \newlabel{rel:euue}{{2.14}{{\reset@font 98}}} \citation{vai} \newlabel{thdeg-x}{{20}{{\reset@font 99}}} \newlabel{rel:parabola-x}{{2.15}{{\reset@font 99}}} \citation{sh_kol_etal} \citation{sh_kol_etal} \citation{klles2} \newlabel{f:qdisk}{{2.16}{{\reset@font 101}}} \newlabel{rel:unitary}{{2.17}{{\reset@font 103}}} \@writefile{toc}{\contentsline {section}{\numberline {2.2}Some classes of $*$-algebras with 3 and 4 generators}{{\reset@font 105}}} \newlabel{sec:2.2}{{2.2}{{\reset@font 105}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Representations of graded $so(3)$ and four-tup\discretionary {-}{}{}les of projections satisfying a linear relation}{{\reset@font 105}}} \newlabel{sec:2.2.1}{{2.2.1}{{\reset@font 105}}} \newlabel{graded-so3}{{2.18}{{\reset@font 105}}} \newlabel{th:gleb}{{22}{{\reset@font 106}}} \newlabel{graded-su2}{{2.19}{{\reset@font 107}}} \newlabel{proj-gen}{{2.20}{{\reset@font 109}}} \newlabel{proj-4}{{2.21}{{\reset@font 109}}} \newlabel{rel:four-center}{{2.22}{{\reset@font 112}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Representations of a class of quadratic algebras with three generators}{{\reset@font 112}}} \newlabel{sec:2.2.2}{{2.2.2}{{\reset@font 112}}} \newlabel{three-gen}{{2.23}{{\reset@font 113}}} \newlabel{rel:recurse}{{2.24}{{\reset@font 113}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}Operator relations connected with a dynamical system on a plane}{{\reset@font 115}}} \newlabel{sec:2.2.3}{{2.2.3}{{\reset@font 115}}} \newlabel{d2}{{2.25}{{\reset@font 115}}} \newlabel{d4}{{2.26}{{\reset@font 115}}} \newlabel{bprop}{{39}{{\reset@font 116}}} \newlabel{three-fock}{{40}{{\reset@font 116}}} \newlabel{three-uni}{{41}{{\reset@font 117}}} \citation{103} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.4}Representation of real forms of Witten's first deformation}{{\reset@font 118}}} \newlabel{sec:2.2.4}{{2.2.4}{{\reset@font 118}}} \newlabel{witt3}{{2.27}{{\reset@font 118}}} \newlabel{witt4}{{2.28}{{\reset@font 119}}} \newlabel{witt5}{{2.29}{{\reset@font 119}}} \newlabel{witt7}{{2.30}{{\reset@font 119}}} \citation{sklyan} \citation{kul_re} \citation{drinf} \citation{jimbo} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.5}Representations of the Sklyanin algebra and $U_q(sl(2))$}{{\reset@font 122}}} \newlabel{sec:2.2.5}{{2.2.5}{{\reset@font 122}}} \newlabel{rel_sklyanin}{{2.31}{{\reset@font 122}}} \citation{masuda_etal} \newlabel{vos}{{2.32}{{\reset@font 128}}} \newlabel{pat}{{32}{{\reset@font 130}}} \citation{fai} \@writefile{toc}{\contentsline {section}{\numberline {2.3}Representations of $q$-deformed $U(so(3,{\@mathbb C}))$}{{\reset@font 132}}} \newlabel{sec:2.3}{{2.3}{{\reset@font 132}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}Real forms of $U_q(so(3, {\@mathbb C}))$}{{\reset@font 132}}} \newlabel{sec:2.3.1}{{2.3.1}{{\reset@font 132}}} \newlabel{soq3}{{2.33}{{\reset@font 132}}} \newlabel{th-inv1-eq}{{47}{{\reset@font 133}}} \newlabel{rel:Mq2}{{2.34}{{\reset@font 133}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}Representations of $U_q(so(3,\@mathbb C))$}{{\reset@font 134}}} \newlabel{sec:2.3.2}{{2.3.2}{{\reset@font 134}}} \newlabel{rel:soq3I}{{2.35}{{\reset@font 134}}} \newlabel{rel:soq3II}{{2.36}{{\reset@font 134}}} \newlabel{th1}{{33}{{\reset@font 134}}} \newlabel{supp}{{2.37}{{\reset@font 135}}} \newlabel{dynrel}{{2.38}{{\reset@font 136}}} \newlabel{th2}{{34}{{\reset@font 137}}} \newlabel{dynrel4}{{2.39}{{\reset@font 138}}} \newlabel{th:soq3root}{{35}{{\reset@font 139}}} \newlabel{supp1}{{2.40}{{\reset@font 142}}} \newlabel{ff2}{{2.41}{{\reset@font 143}}} \newlabel{gr1}{{2.42}{{\reset@font 144}}} \newlabel{ff10}{{2.43}{{\reset@font 144}}} \newlabel{gr2}{{2.44}{{\reset@font 146}}} \newlabel{f30}{{2.45}{{\reset@font 147}}} \newlabel{gr3}{{2.46}{{\reset@font 149}}} \newlabel{ss}{{2.47}{{\reset@font 149}}} \citation{100} \@writefile{toc}{\contentsline {section}{\numberline {2.4}Many-dimensional dynamical systems}{{\reset@font 150}}} \newlabel{sec:2.4}{{2.4}{{\reset@font 150}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}``Direct products'' of one-dimensional dynamical systems}{{\reset@font 151}}} \newlabel{sec:2.4.1}{{2.4.1}{{\reset@font 151}}} \newlabel{gather:dirpr}{{2.48}{{\reset@font 151}}} \newlabel{align:dirpr}{{2.49}{{\reset@font 152}}} \newlabel{align:dsdp}{{2.4.1}{{\reset@font 152}}} \citation{pusz_anti} \citation{pw} \citation{jorg} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.2}``Triangular'' dynamical systems.}{{\reset@font 154}}} \newlabel{sec:2.4.2}{{2.4.2}{{\reset@font 154}}} \newlabel{align:muccr}{{2.51}{{\reset@font 155}}} \newlabel{ccr-klein}{{51}{{\reset@font 155}}} \newlabel{gather:dsmucc}{{2.52}{{\reset@font 156}}} \newlabel{car-klein}{{36}{{\reset@font 158}}} \newlabel{align:muc}{{2.53}{{\reset@font 158}}} \newlabel{gather:pos}{{2.4.2}{{\reset@font 158}}} \newlabel{align:wt}{{2.4.2}{{\reset@font 159}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.3}Operator relations connected with many-dimen\discretionary {-}{}{}si\discretionary {-}{}{}onal dynamical systems}{{\reset@font 160}}} \newlabel{sec:2.4.3}{{2.4.3}{{\reset@font 160}}} \citation{ostur} \newlabel{rels-multi}{{2.56}{{\reset@font 161}}} \newlabel{rels-cu}{{2.57}{{\reset@font 161}}} \citation{ostur} \newlabel{rels-ds}{{2.58}{{\reset@font 162}}} \newlabel{ds-commute}{{2.59}{{\reset@font 162}}} \citation{ostur} \newlabel{lemma2}{{11}{{\reset@font 163}}} \citation{ostur} \citation{noumi} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.4}Representations of the non-standard real quantum sphere}{{\reset@font 165}}} \newlabel{sec:2.4.4}{{2.4.4}{{\reset@font 165}}} \newlabel{sphere}{{2.62}{{\reset@font 165}}} \newlabel{qsphere}{{2.63}{{\reset@font 165}}} \citation{wor} \citation{vakskor} \citation{woraff} \citation{wor} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.5}Heisenberg relations for the quantum $E(2)$\penalty -\@M group}{{\reset@font 168}}} \newlabel{sec:2.4.5}{{2.4.5}{{\reset@font 168}}} \citation{wor} \citation{wor} \newlabel{e2}{{2.64}{{\reset@font 169}}} \newlabel{coe2}{{2.65}{{\reset@font 169}}} \newlabel{heis}{{2.66}{{\reset@font 169}}} \newlabel{ds}{{2.67}{{\reset@font 170}}} \citation{jorg} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.6}Wick algebras related to dynamical systems}{{\reset@font 172}}} \newlabel{sec:2.4.6}{{2.4.6}{{\reset@font 172}}} \citation{jorg} \newlabel{commutation_rule}{{2.68}{{\reset@font 173}}} \newlabel{wick-proj}{{55}{{\reset@font 173}}} \newlabel{eq:max}{{2.69}{{\reset@font 174}}} \newlabel{eqnarray:main}{{2.70}{{\reset@font 175}}} \newlabel{remark:posm}{{44}{{\reset@font 176}}} \newlabel{proposition:cal}{{57}{{\reset@font 176}}} \newlabel{align:sys}{{2.71}{{\reset@font 177}}} \@writefile{toc}{\contentsline {section}{\numberline {2.5}On representations of some nuclear algebras}{{\reset@font 179}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5.1}Commutative models}{{\reset@font 179}}} \newlabel{sec:2.5.1}{{2.5.1}{{\reset@font 179}}} \newlabel{model:uni}{{2.72}{{\reset@font 179}}} \newlabel{model:uni2}{{2.73}{{\reset@font 181}}} \citation{bos} \citation{umz88} \newlabel{models-relations}{{2.74}{{\reset@font 182}}} \newlabel{model-common}{{45}{{\reset@font 183}}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5.2}Centered operators}{{\reset@font 184}}} \newlabel{sec:2.5.2}{{2.5.2}{{\reset@font 184}}} \newlabel{cent}{{2.76}{{\reset@font 184}}} \newlabel{im}{{2.77}{{\reset@font 184}}} \newlabel{f1}{{2.78}{{\reset@font 185}}} \newlabel{f2}{{2.79}{{\reset@font 185}}} \newlabel{thmodel}{{46}{{\reset@font 186}}} \newlabel{model}{{2.80}{{\reset@font 186}}} \newlabel{thdeg}{{47}{{\reset@font 186}}} \citation{dye} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5.3}Representations of Cuntz algebras}{{\reset@font 188}}} \newlabel{cuntz_model}{{2.82}{{\reset@font 188}}} \newlabel{cuntz_ds}{{2.83}{{\reset@font 189}}} \citation{book} \citation{ber1} \citation{brat-jorg} \newlabel{cuntz-alpha}{{2.85}{{\reset@font 193}}} \newlabel{cuntz-aux}{{2.86}{{\reset@font 194}}} \newlabel{cuntz-aux2}{{2.87}{{\reset@font 195}}} \citation{macf} \citation{biede} \citation{damku} \citation{kul} \citation{klles} \citation{klles2} \citation{greek} \citation{vai} \citation{romp} \citation{vai} \citation{vaisam1} \citation{vai_sam_sel} \citation{mackey1} \citation{efr} \citation{tomi} \citation{renau} \citation{arz_ver2} \citation{mormu} \citation{tomi} \citation{vaisam1} \citation{vai_sam_sel} \citation{vai_fed} \@writefile{toc}{\contentsline {section}{Comments to Chapter 2}{{\reset@font 197}}} \citation{efr} \citation{vai_sam_sel} \citation{shmr} \citation{sh_kol_etal} \citation{83} \citation{mormu} \citation{vo_mfat} \citation{sh_kol_etal} \citation{vaisam1} \citation{zachos} \citation{book} \citation{gorpod} \citation{ossilv} \citation{besp_umz} \citation{gal_mfat} \citation{besp_umz} \citation{gorpod} \citation{gal_mur} \citation{rab_sam_fa} \citation{three} \citation{vaisam1} \citation{pop_snmp} \citation{sklyan} \citation{skl_2} \citation{klim_sch} \citation{kor_soi} \citation{vai3} \citation{odes_fei} \citation{fai} \citation{odes} \citation{fai} \citation{108} \citation{107} \citation{100} \citation{gorpod} \citation{bagro_kru} \citation{bagro_kru} \citation{107} \citation{108} \citation{100} \citation{139} \citation{100} \citation{jorg} \citation{102} \citation{pw} \citation{pusz_anti} \citation{jorg} \citation{proskurin} \citation{ostur} \citation{noumi} \citation{ostur} \citation{wor} \citation{umz95} \citation{wor} \citation{jorg} \citation{jorg} \citation{proskurin} \citation{mackey1} \citation{mackey} \citation{gar_w_car} \citation{gar_w_ccr} \citation{araki60} \citation{gel} \citation{gol} \citation{heg_mel} \citation{str_voi} \citation{ver_gel_g2} \citation{men_shar} \citation{goldin} \citation{isma} \citation{ver_gel_g} \citation{bos} \citation{umz88} \citation{romp} \citation{berkon} \citation{mormu} \citation{arv89} \citation{lac} \citation{jor} \citation{bra_jor1} \citation{bra_jor2} \citation{brat-jorg} \@writefile{toc}{\contentsline {chapter}{\numberline {3}On the complexity of the description of representations of \hbox {$*$-}algebras}{{\reset@font 202}}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {3.1}$*$-Wild algebras and relations}{{\reset@font 202}}} \newlabel{sec:3.1}{{3.1}{{\reset@font 202}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}Majorization of $*$-algebras with respect to the complexity of their representations}{{\reset@font 202}}} \newlabel{sec:3.1.1}{{3.1.1}{{\reset@font 202}}} \citation{kru_wor} \newlabel{majoriz}{{13}{{\reset@font 205}}} \citation{take79} \citation{murphy} \newlabel{bound}{{50}{{\reset@font 206}}} \citation{15} \newlabel{th:main_major}{{51}{{\reset@font 208}}} \newlabel{cor:q-order}{{8}{{\reset@font 210}}} \citation{ols_zame} \citation{rab_umz} \citation{89} \citation{krusam} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}$*$-Wildness of $*$-algebras}{{\reset@font 211}}} \newlabel{sec:3.1.2}{{3.1.2}{{\reset@font 211}}} \citation{117} \newlabel{th_o}{{52}{{\reset@font 212}}} \newlabel{th_t}{{53}{{\reset@font 213}}} \newlabel{def:14}{{14}{{\reset@font 213}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.3}$*$-Wild algebras generated by orthogonal projections and idempotents}{{\reset@font 213}}} \newlabel{sec:3.1.3}{{3.1.3}{{\reset@font 213}}} \newlabel{th:anti-wild}{{55}{{\reset@font 214}}} \citation{krusam} \newlabel{th_f}{{57}{{\reset@font 215}}} \citation{112} \citation{113} \newlabel{th_fv}{{58}{{\reset@font 218}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.4}$*$-Wild semilinear relations}{{\reset@font 220}}} \newlabel{sec:3.1.4}{{3.1.4}{{\reset@font 220}}} \newlabel{poly}{{3.1}{{\reset@font 220}}} \newlabel{pro:wild1}{{67}{{\reset@font 220}}} \newlabel{pro:wild2}{{68}{{\reset@font 221}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.5}$*$-Wild quadratic and cubic relations}{{\reset@font 221}}} \newlabel{sec:3.1.5}{{3.1.5}{{\reset@font 221}}} \newlabel{quadr1}{{60}{{\reset@font 222}}} \newlabel{cub}{{3.3}{{\reset@font 222}}} \newlabel{tri}{{3.4}{{\reset@font 223}}} \newlabel{sis}{{3.5}{{\reset@font 224}}} \newlabel{th:cub1}{{61}{{\reset@font 225}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.6}$*$-Wild groups. Periodic groups are not $*$-wild}{{\reset@font 226}}} \newlabel{sec:3.1.6}{{3.1.6}{{\reset@font 226}}} \newlabel{pr:wildgroups}{{71}{{\reset@font 226}}} \citation{kiril} \citation{olsh} \citation{adjan_book} \citation{ern} \newlabel{th:kal}{{62}{{\reset@font 228}}} \@writefile{toc}{\contentsline {section}{\numberline {3.2}On the complexity of the description of classes of non self-adjoint operators}{{\reset@font 228}}} \newlabel{sec:3.2}{{3.2}{{\reset@font 228}}} \newlabel{rel:pxx}{{3.6}{{\reset@font 229}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2.1}Classes of non self-adjoint operators singled out by a quadratic or a cubic relation}{{\reset@font 229}}} \newlabel{sec:3.2.1}{{3.2.1}{{\reset@font 229}}} \newlabel{cond}{{3.7}{{\reset@font 230}}} \newlabel{polynom2}{{3.8}{{\reset@font 230}}} \newlabel{quadr2}{{63}{{\reset@font 230}}} \citation{91} \citation{halm2} \newlabel{qpline}{{3.9}{{\reset@font 231}}} \newlabel{qupline}{{3.10}{{\reset@font 231}}} \newlabel{a2b}{{3.11}{{\reset@font 232}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2.2}Partial isometries, weakly centered operators and algebraic operators}{{\reset@font 233}}} \newlabel{sec:3.2.2}{{3.2.2}{{\reset@font 233}}} \citation{besp_mfat} \newlabel{th:wcpi}{{67}{{\reset@font 234}}} \citation{wog} \newlabel{cor7}{{73}{{\reset@font 235}}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2.3}Hyponormal operators and pairs of commuting completely non-unitary isometries}{{\reset@font 235}}} \newlabel{sec:3.2.3}{{3.2.3}{{\reset@font 235}}} \citation{sam_tur} \citation{89} \citation{aus} \citation{gab_roi_book} \citation{krusam} \citation{84} \citation{pirsam} \citation{85} \citation{kru_sam98} \citation{kru_sam_ams} \@writefile{toc}{\contentsline {section}{Comments to Chapter 3}{{\reset@font 237}}} \citation{rief74} \citation{43} \citation{lance95} \citation{drozd} \citation{89} \citation{86} \citation{bagro_kru_2} \citation{besp_mfat} \citation{krusam} \citation{kru_sam98} \citation{kru_sam_ams} \citation{bss} \citation{sam_tur_sh} \citation{krusam} \citation{kal_sam} \citation{roi_box} \citation{84} \citation{serg87} \citation{ols_zame} \citation{rab_umz} \citation{91} \citation{brown} \citation{halm_mac} \citation{pear} \citation{wog_2} \citation{wog} \citation{benk} \citation{benk_ii} \citation{benk_iii} \citation{camp} \citation{91} \citation{halm2} \citation{halm_mac} \citation{halm2} \citation{85} \citation{piryat} \citation{bessam1} \citation{besp_mfat} \citation{wog} \citation{berg_cob_leb} \bibdata{ref,new,2} \bibcite{abdes}{1} \bibcite{adjan_book}{2} \bibcite{akhi_book}{3} \bibcite{akh_glaz}{4} \bibcite{126}{5} \bibcite{araki60}{6} \bibcite{54}{7} \bibcite{56}{8} \bibcite{arv76}{9} \bibcite{13}{10} \bibcite{arv89}{11} \bibcite{arz_ver2}{12} \bibcite{aus}{13} \bibcite{azi_io}{14} \bibcite{90}{15} \bibcite{bagro_kru_2}{16} \@writefile{toc}{\contentsline {section}{Bibliography}{{\reset@font 241}}} \bibcite{bagro_kru}{17} \bibcite{barn}{18} \bibcite{bart}{19} \bibcite{59}{20} \bibcite{benk}{21} \bibcite{benk_ii}{22} \bibcite{benk_iii}{23} \bibcite{ber0}{24} \bibcite{ber1}{25} \bibcite{berkon}{26} \bibcite{65}{27} \bibcite{bos}{28} \bibcite{ber_us_sh}{29} \bibcite{68}{30} \bibcite{berg_cob_leb}{31} \bibcite{besp_umz}{32} \bibcite{besp_mfat}{33} \bibcite{bessam1}{34} \bibcite{bss}{35} \bibcite{biede}{36} \bibcite{69}{37} \bibcite{black}{38} \bibcite{bon_dr}{39} \bibcite{116}{40} \bibcite{121}{41} \bibcite{boz_sp91}{42} \bibcite{102}{43} \bibcite{bra_jor2}{44} \bibcite{jor}{45} \bibcite{brat-jorg}{46} \bibcite{bra_jor1}{47} \bibcite{70}{48} \bibcite{91}{49} \bibcite{brown}{50} \bibcite{43}{51} \bibcite{bukl2}{52} \bibcite{camp}{53} \bibcite{chari}{54} \bibcite{21}{55} \bibcite{29}{56} \bibcite{conn}{57} \bibcite{cuntz}{58} \bibcite{cur_re}{59} \bibcite{dal}{60} \bibcite{73}{61} \bibcite{damku}{62} \bibcite{greek}{63} \bibcite{34}{64} \bibcite{111}{65} \bibcite{quesne3}{66} \bibcite{quesne}{67} \bibcite{78}{68} \bibcite{112}{69} \bibcite{89}{70} \bibcite{dor_bel}{71} \bibcite{douglas}{72} \bibcite{drinf}{73} \bibcite{drozd}{74} \bibcite{dye}{75} \bibcite{dyk_nica}{76} \bibcite{efr}{77} \bibcite{7}{78} \bibcite{ern}{79} \bibcite{fai}{80} \bibcite{finck}{81} \bibcite{flato}{82} \bibcite{16}{83} \bibcite{gar_w_car}{84} \bibcite{gar_w_ccr}{85} \bibcite{gab_roi_book}{86} \bibcite{117}{87} \bibcite{gal_mfat}{88} \bibcite{gal_mur}{89} \bibcite{139}{90} \bibcite{gelpon}{91} \bibcite{127}{92} \bibcite{gel}{93} \bibcite{gli}{94} \bibcite{goh_etal}{95} \bibcite{goh_rei}{96} \bibcite{goldin}{97} \bibcite{gol}{98} \bibcite{19}{99} \bibcite{goodman}{100} \bibcite{gorpod}{101} \bibcite{halm2}{102} \bibcite{halm1}{103} \bibcite{halm_mac}{104} \bibcite{77}{105} \bibcite{76}{106} \bibcite{107}{107} \bibcite{108}{108} \bibcite{heb_etal}{109} \bibcite{heg_mel}{110} \bibcite{31}{111} \bibcite{holevo}{112} \bibcite{113}{113} \bibcite{inoue}{114} \bibcite{isma}{115} \bibcite{32}{116} \bibcite{jant}{117} \bibcite{jimbo}{118} \bibcite{jones89}{119} \bibcite{110}{120} \bibcite{jorg_book}{121} \bibcite{jor_moore}{122} \bibcite{jorg_s_w}{123} \bibcite{jorg}{124} \bibcite{jorg_wer}{125} \bibcite{kac}{126} \bibcite{kad_rin}{127} \bibcite{kal_sam}{128} \bibcite{kaz}{129} \bibcite{118}{130} \bibcite{kiril2}{131} \bibcite{kiril}{132} \bibcite{kis_sh}{133} \bibcite{kleinecke}{134} \bibcite{klles}{135} \bibcite{klles2}{136} \bibcite{klim_sch}{137} \bibcite{koe}{138} \bibcite{koor_sw}{139} \bibcite{kor_soi}{140} \bibcite{krugl_q}{141} \bibcite{84}{142} \bibcite{85}{143} \bibcite{krusam}{144} \bibcite{kru_sam98}{145} \bibcite{kru_sam_ams}{146} \bibcite{142}{147} \bibcite{kru_r_s}{148} \bibcite{125}{149} \bibcite{kru_wor}{150} \bibcite{kul}{151} \bibcite{kul_re}{152} \bibcite{lac}{153} \bibcite{lance95}{154} \bibcite{10}{155} \bibcite{17}{156} \bibcite{lus}{157} \bibcite{macf}{158} \bibcite{mackey1}{159} \bibcite{mackey}{160} \bibcite{mad1}{161} \bibcite{manin2}{162} \bibcite{masuda_etal}{163} \bibcite{20}{164} \bibcite{rodm2}{165} \bibcite{men_shar}{166} \bibcite{mis}{167} \bibcite{mormu}{168} \bibcite{murphy}{169} \bibcite{murneu}{170} \bibcite{nagy_nica2}{171} \bibcite{naz}{172} \bibcite{nelson}{173} \bibcite{newt}{174} \bibcite{niz_tur}{175} \bibcite{noumi}{176} \bibcite{odes}{177} \bibcite{odes_fei}{178} \bibcite{ols_zame}{179} \bibcite{olsh}{180} \bibcite{three}{181} \bibcite{vo_mfat}{182} \bibcite{umz88}{183} \bibcite{fa}{184} \bibcite{lomi}{185} \bibcite{romp}{186} \bibcite{adv}{187} \bibcite{slie}{188} \bibcite{umz95}{189} \bibcite{non}{190} \bibcite{romp2}{191} \bibcite{ossilv}{192} \bibcite{ostur}{193} \bibcite{partas}{194} \bibcite{pear}{195} \bibcite{ped2}{196} \bibcite{28}{197} \bibcite{ped}{198} \bibcite{15}{199} \bibcite{33}{200} \bibcite{piryat}{201} \bibcite{pirsam}{202} \bibcite{pop_snmp}{203} \bibcite{pop_mfat}{204} \bibcite{pow_i}{205} \bibcite{pow}{206} \bibcite{30}{207} \bibcite{proskurin}{208} \bibcite{pro_mfat}{209} \bibcite{pro}{210} \bibcite{pusz_anti}{211} \bibcite{pw}{212} \bibcite{36}{213} \bibcite{rab_mfat}{214} \bibcite{rab_umz}{215} \bibcite{rab_sam_mfat}{216} \bibcite{rab_sam_ieot}{217} \bibcite{rab_sam_fa}{218} \bibcite{115}{219} \bibcite{reedsim}{220} \bibcite{renau}{221} \bibcite{rief_book}{222} \bibcite{rief74}{223} \bibcite{124}{224} \bibcite{roi_box}{225} \bibcite{137}{226} \bibcite{sak}{227} \bibcite{book}{228} \bibcite{sam_sh_umz}{229} \bibcite{sam_tur}{230} \bibcite{100}{231} \bibcite{119}{232} \bibcite{sam_tur_sh}{233} \bibcite{135}{234} \bibcite{133}{235} \bibcite{132}{236} \bibcite{134}{237} \bibcite{shwe_we}{238} \bibcite{serg84}{239} \bibcite{serg87}{240} \bibcite{serg90}{241} \bibcite{serg92}{242} \bibcite{86}{243} \bibcite{shapiro}{244} \bibcite{shmr}{245} \bibcite{sh_kol_etal}{246} \bibcite{shirokov}{247} \bibcite{143}{248} \bibcite{82}{249} \bibcite{81}{250} \bibcite{silv}{251} \bibcite{83}{252} \bibcite{sin}{253} \bibcite{sklyan}{254} \bibcite{skl_2}{255} \bibcite{smst}{256} \bibcite{138}{257} \bibcite{str_voi}{258} \bibcite{take79}{259} \bibcite{tam}{260} \bibcite{11}{261} \bibcite{thoma}{262} \bibcite{tomi}{263} \bibcite{26}{264} \bibcite{144}{265} \bibcite{130}{266} \bibcite{vakskor}{267} \bibcite{vas}{268} \bibcite{vasi}{269} \bibcite{vasil}{270} \bibcite{114}{271} \bibcite{vai3}{272} \bibcite{vai}{273} \bibcite{vai_fed}{274} \bibcite{vaisam1}{275} \bibcite{vai_sam_sel}{276} \bibcite{ver}{277} \bibcite{ver_gel_g2}{278} \bibcite{ver_gel_g}{279} \bibcite{voi_dy_ni}{280} \bibcite{yzette}{281} \bibcite{wen}{282} \bibcite{wich}{283} \bibcite{wielandt}{284} \bibcite{103}{285} \bibcite{wog_2}{286} \bibcite{wog}{287} \bibcite{wor87}{288} \bibcite{wor}{289} \bibcite{woraff}{290} \bibcite{wor_aff_2}{291} \bibcite{yama}{292} \bibcite{zachos}{293} \bibcite{zak}{294} \bibcite{zhe}{295} \bibcite{zhel}{296} \bibstyle{amsplain}
Simpan