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
/
final
/
Edit File:
the.aux
\relax \@writefile{toc}{{\bf Introduction to the Theory of Representations of Finitely Presented $*$-Algebras.\\ I. Representations by bounded operators}\\ V. Ostrovskyi, Yu. Samoilenko\vskip 5pt} \@writefile{toc}{\contentsline {chapter}{Preface}{3}} \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}{7}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {1.1}Introduction to representations of $*$-algebras}{7}} \newlabel{sec:1.1}{{1.1}{7}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}$*$-Representations: key words}{7}} \newlabel{sec:1.1.1}{{1.1.1}{7}} \newlabel{intertwine}{{1.1}{8}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.2}$C^*$-representable $*$-algebras}{11}} \newlabel{sec:1.1.2}{{1.1.2}{11}} \newlabel{prop:cstar}{{5}{12}} \citation{wich} \citation{dor_bel} \citation{29} \citation{21} \citation{30} \citation{77} \newlabel{rem:resid}{{3}{15}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.3}Enveloping $*$-algebras and $C^*$-algebras}{15}} \newlabel{sec:1.1.3}{{1.1.3}{15}} \citation{117} \citation{114} \citation{115} \newlabel{ex:proj}{{3}{17}} \citation{kru_wor} \citation{15} \citation{13} \newlabel{WSW}{{2}{19}} \newlabel{env}{{1}{19}} \citation{16} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.4}$*$-Representations of generators and relations}{21}} \newlabel{sec:1.1.4}{{1.1.4}{21}} \newlabel{just_relations}{{1.4}{21}} \newlabel{self_relation}{{1.5}{21}} \citation{reedsim} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.5}Pairs of self-adjoint operators satisfying quad\discretionary {-}{}{}ratic relations}{24}} \newlabel{sec:1.1.5}{{1.1.5}{24}} \newlabel{oneone}{{1.1.5}{24}} \newlabel{onetwo}{{1.7}{24}} \citation{126} \@writefile{toc}{\contentsline {section}{\numberline {1.2}$F_n$-algebras and their representations}{27}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}About $*$-representations of ${F}_n$-algebras}{27}} \newlabel{sec:1.2.1}{{1.2.1}{27}} \newlabel{th:r.f}{{2}{27}} \citation{142} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}Examples of ${F}_n$-algebras generated by idempotents and their representations}{29}} \newlabel{sec:1.2.2}{{1.2.2}{29}} \citation{naz} \citation{127} \citation{121} \citation{bon_dr} \citation{124} \citation{125} \citation{119} \newlabel{th:q2}{{3}{35}} \@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}{39}} \newlabel{sec:1.2.3}{{1.2.3}{39}} \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}{42}} \newlabel{sec:1.3}{{1.3}{42}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Representations of two-dimensional real Lie algebras and their nonlinear transformations by bounded operators}{42}} \newlabel{sec:1.3.1}{{1.3.1}{42}} \newlabel{deformedlie}{{1.8}{42}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Pairs of operators connected by semilinear relations}{44}} \newlabel{sec:1.3.2}{{1.3.2}{44}} \citation{sam_tur_sh} \newlabel{sr}{{1.9}{45}} \newlabel{hom}{{1.10}{45}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Kleinecke--Shirokov type theorems}{48}} \newlabel{sec:1.3.3}{{1.3.3}{48}} \newlabel{pr1}{{19}{48}} \newlabel{def1}{{3}{49}} \newlabel{th1-semi}{{6}{49}} \citation{137} \newlabel{th2-semi}{{7}{50}} \newlabel{p20'}{{1.11}{50}} \newlabel{p20}{{1.12}{51}} \newlabel{l1}{{5}{51}} \newlabel{l2}{{6}{52}} \newlabel{cth2}{{8}{52}} \newlabel{p21}{{1.14}{53}} \newlabel{p22}{{1.15}{53}} \citation{143} \newlabel{c1}{{9}{54}} \citation{137} \citation{143} \newlabel{c2}{{10}{55}} \newlabel{gr}{{11}{55}} \newlabel{c4}{{1}{56}} \newlabel{ex}{{7}{56}} \newlabel{prp}{{1.17}{57}} \newlabel{mul}{{1.18}{58}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Irreducible representations of semilinear relations}{60}} \newlabel{sec:1.3.4}{{1.3.4}{60}} \newlabel{connec}{{20}{60}} \newlabel{pr4}{{22}{62}} \newlabel{therg}{{23}{63}} \newlabel{mk}{{1.19}{63}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.5}Representations of semilinear ${F}_4$-relations}{66}} \newlabel{sec:1.3.5}{{1.3.5}{66}} \@writefile{toc}{\contentsline {section}{\numberline {1.4}Representations of $q$-relations}{68}} \newlabel{sec:1.4}{{1.4}{68}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Finite-dimensional representations of $q$-re\discretionary {-}{}{}la\discretionary {-}{}{}ti\discretionary {-}{}{}ons}{68}} \newlabel{sec:1.4.1}{{1.4.1}{68}} \newlabel{prop:ssh}{{25}{68}} \citation{sam_sh_umz} \newlabel{prop:ssh1}{{26}{69}} \newlabel{skew1}{{1.20}{69}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}Hermitian $q$-plane and $q$-CCR}{70}} \newlabel{sec:1.4.2}{{1.4.2}{70}} \citation{adv} \newlabel{q-plane}{{1.21}{71}} \newlabel{q-plane_ii}{{1.22}{71}} \citation{ber0} \newlabel{alpha-ccr}{{1.23}{72}} \newlabel{alpha-ccr2}{{1.24}{72}} \newlabel{q-ccr}{{1.25}{72}} \citation{ber0} \citation{bukl2} \newlabel{ds-qccr}{{1.26}{73}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.3}Real quantum plane and real quantum hyperboloid}{75}} \newlabel{sec:1.4.3}{{1.4.3}{75}} \newlabel{hyperb}{{1.27}{76}} \citation{133} \citation{132} \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} \newlabel{hyperb1}{{1.28}{77}} \@writefile{toc}{\contentsline {section}{Comments to Chapter 1}{77}} \citation{21} \citation{30} \citation{77} \citation{78} \citation{118} \citation{114} \citation{115} \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}{83}} \@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}{83}} \newlabel{sec:2.1}{{2.1}{83}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}Operator relations connected with one-dimen\discretionary {-}{}{}sional dynamical systems}{83}} \newlabel{sec:2.1.1}{{2.1.1}{83}} \newlabel{xx}{{2.1}{83}} \citation{klles} \newlabel{rel:quadratic}{{2.2}{84}} \newlabel{rel:parabola}{{2.3}{84}} \newlabel{ucu}{{2.4}{85}} \newlabel{cu}{{2.5}{85}} \newlabel{xx_fun}{{2.6}{85}} \newlabel{xx_n}{{2.7}{85}} \newlabel{cu-props}{{28}{85}} \newlabel{xx-center}{{29}{86}} \newlabel{toeigen}{{30}{88}} \newlabel{rel:chains}{{2.8}{88}} \citation{vai_fed} \newlabel{th:per}{{15}{91}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}Finite-dimensional representations}{91}} \newlabel{sec:2.1.2}{{2.1.2}{91}} \newlabel{fin_th}{{16}{91}} \newlabel{one5}{{2.9}{92}} \citation{shmr} \newlabel{moebius-rel}{{12}{95}} \citation{83} \newlabel{moebius-map}{{2.12}{96}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.3}Infinite-dimensional representations}{96}} \newlabel{sec:2.1.3}{{2.1.3}{96}} \newlabel{thiso-x}{{18}{97}} \newlabel{iso2-x}{{2.13}{98}} \newlabel{thirr-x}{{19}{98}} \newlabel{rel:euue}{{2.14}{99}} \citation{vai} \newlabel{thdeg-x}{{20}{100}} \newlabel{rel:parabola-x}{{2.15}{100}} \citation{sh_kol_etal} \citation{sh_kol_etal} \citation{klles2} \newlabel{f:qdisk}{{2.16}{102}} \newlabel{rel:unitary}{{2.17}{104}} \@writefile{toc}{\contentsline {section}{\numberline {2.2}Some classes of $*$-algebras with 3 and 4 generators}{106}} \newlabel{sec:2.2}{{2.2}{106}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Representations of graded $so(3)$ and four-tup\discretionary {-}{}{}les of projections satisfying a linear relation}{106}} \newlabel{sec:2.2.1}{{2.2.1}{106}} \newlabel{graded-so3}{{2.18}{106}} \newlabel{th:gleb}{{22}{107}} \newlabel{graded-su2}{{2.19}{108}} \newlabel{proj-gen}{{2.20}{110}} \newlabel{proj-4}{{2.21}{110}} \newlabel{rel:four-center}{{2.22}{113}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Representations of a class of quadratic algebras with three generators}{113}} \newlabel{sec:2.2.2}{{2.2.2}{113}} \newlabel{three-gen}{{2.23}{114}} \newlabel{rel:recurse}{{2.24}{114}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}Operator relations connected with a dynamical system on a plane}{116}} \newlabel{sec:2.2.3}{{2.2.3}{116}} \newlabel{d2}{{2.25}{116}} \newlabel{d4}{{2.26}{116}} \newlabel{bprop}{{39}{117}} \newlabel{three-fock}{{40}{117}} \newlabel{three-uni}{{41}{118}} \citation{103} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.4}Representation of real forms of Witten's first deformation}{119}} \newlabel{sec:2.2.4}{{2.2.4}{119}} \newlabel{witt3}{{2.27}{119}} \newlabel{witt4}{{2.28}{120}} \newlabel{witt5}{{2.29}{120}} \newlabel{witt7}{{2.30}{120}} \citation{sklyan} \citation{kul_re} \citation{drinf} \citation{jimbo} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.5}Representations of the Sklyanin algebra and $U_q(sl(2))$}{123}} \newlabel{sec:2.2.5}{{2.2.5}{123}} \newlabel{rel_sklyanin}{{2.31}{123}} \citation{masuda_etal} \newlabel{vos}{{2.32}{129}} \newlabel{pat}{{32}{131}} \citation{fai} \@writefile{toc}{\contentsline {section}{\numberline {2.3}Representations of $q$-deformed $U(so(3,{\@mathbb C}))$}{133}} \newlabel{sec:2.3}{{2.3}{133}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}Real forms of $U_q(so(3, {\@mathbb C}))$}{133}} \newlabel{sec:2.3.1}{{2.3.1}{133}} \newlabel{soq3}{{2.33}{133}} \newlabel{th-inv1-eq}{{47}{134}} \newlabel{rel:Mq2}{{2.34}{134}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}Representations of $U_q(so(3,\@mathbb C))$}{135}} \newlabel{sec:2.3.2}{{2.3.2}{135}} \newlabel{rel:soq3I}{{2.35}{135}} \newlabel{rel:soq3II}{{2.36}{135}} \newlabel{th1}{{33}{135}} \newlabel{supp}{{2.37}{136}} \newlabel{dynrel}{{2.38}{137}} \newlabel{th2}{{34}{138}} \newlabel{dynrel4}{{2.39}{139}} \newlabel{th:soq3root}{{35}{140}} \newlabel{supp1}{{2.40}{143}} \newlabel{ff2}{{2.41}{144}} \newlabel{gr1}{{2.42}{145}} \newlabel{ff10}{{2.43}{145}} \newlabel{gr2}{{2.44}{147}} \newlabel{f30}{{2.45}{148}} \newlabel{gr3}{{2.46}{150}} \newlabel{ss}{{2.47}{150}} \citation{100} \@writefile{toc}{\contentsline {section}{\numberline {2.4}Many-dimensional dynamical systems}{151}} \newlabel{sec:2.4}{{2.4}{151}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}``Direct products'' of one-dimensional dynamical systems}{152}} \newlabel{sec:2.4.1}{{2.4.1}{152}} \newlabel{gather:dirpr}{{2.48}{152}} \newlabel{align:dirpr}{{2.49}{153}} \newlabel{align:dsdp}{{2.4.1}{153}} \citation{pusz_anti} \citation{pw} \citation{jorg} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.2}``Triangular'' dynamical systems.}{155}} \newlabel{sec:2.4.2}{{2.4.2}{155}} \newlabel{align:muccr}{{2.51}{155}} \newlabel{ccr-klein}{{51}{156}} \newlabel{gather:dsmucc}{{2.52}{157}} \newlabel{car-klein}{{36}{159}} \newlabel{align:muc}{{2.53}{159}} \newlabel{gather:pos}{{2.4.2}{159}} \newlabel{align:wt}{{2.4.2}{160}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.3}Operator relations connected with many-dimen\discretionary {-}{}{}si\discretionary {-}{}{}onal dynamical systems}{161}} \newlabel{sec:2.4.3}{{2.4.3}{161}} \citation{ostur} \newlabel{rels-multi}{{2.56}{162}} \newlabel{rels-cu}{{2.57}{162}} \citation{ostur} \newlabel{rels-ds}{{2.58}{163}} \newlabel{ds-commute}{{2.59}{163}} \citation{ostur} \newlabel{lemma2}{{11}{164}} \citation{ostur} \citation{noumi} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.4}Representations of the non-standard real quantum sphere}{166}} \newlabel{sec:2.4.4}{{2.4.4}{166}} \newlabel{sphere}{{2.62}{166}} \newlabel{qsphere}{{2.63}{166}} \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}{169}} \newlabel{sec:2.4.5}{{2.4.5}{169}} \citation{wor} \citation{wor} \newlabel{e2}{{2.64}{170}} \newlabel{coe2}{{2.65}{170}} \newlabel{heis}{{2.66}{170}} \newlabel{ds}{{2.67}{171}} \citation{jorg} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.6}Wick algebras related to dynamical systems}{173}} \newlabel{sec:2.4.6}{{2.4.6}{173}} \citation{jorg} \newlabel{commutation_rule}{{2.68}{174}} \newlabel{wick-proj}{{55}{174}} \newlabel{eq:max}{{2.69}{175}} \newlabel{eqnarray:main}{{2.70}{176}} \newlabel{remark:posm}{{44}{177}} \newlabel{proposition:cal}{{57}{177}} \newlabel{align:sys}{{2.71}{178}} \@writefile{toc}{\contentsline {section}{\numberline {2.5}On representations of some nuclear algebras}{180}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5.1}Commutative models}{180}} \newlabel{sec:2.5.1}{{2.5.1}{180}} \newlabel{model:uni}{{2.72}{180}} \newlabel{model:uni2}{{2.73}{182}} \citation{bos} \citation{umz88} \newlabel{models-relations}{{2.74}{183}} \newlabel{model-common}{{45}{184}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5.2}Centered operators}{185}} \newlabel{sec:2.5.2}{{2.5.2}{185}} \newlabel{cent}{{2.76}{185}} \newlabel{im}{{2.77}{185}} \newlabel{f1}{{2.78}{186}} \newlabel{f2}{{2.79}{186}} \newlabel{thmodel}{{46}{187}} \newlabel{model}{{2.80}{187}} \newlabel{thdeg}{{47}{187}} \citation{dye} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5.3}Representations of Cuntz algebras}{189}} \newlabel{cuntz_model}{{2.82}{189}} \newlabel{cuntz_ds}{{2.83}{190}} \citation{book} \citation{ber1} \citation{brat-jorg} \newlabel{cuntz-alpha}{{2.85}{194}} \newlabel{cuntz-aux}{{2.86}{195}} \newlabel{cuntz-aux2}{{2.87}{196}} \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}{198}} \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{klim_sch} \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}{203}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {3.1}$*$-Wild algebras and relations}{203}} \newlabel{sec:3.1}{{3.1}{203}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}Majorization of $*$-algebras with respect to the complexity of their representations}{203}} \newlabel{sec:3.1.1}{{3.1.1}{203}} \citation{kru_wor} \newlabel{majoriz}{{13}{206}} \citation{take79} \citation{murphy} \newlabel{bound}{{50}{207}} \citation{15} \newlabel{th:main_major}{{51}{209}} \newlabel{cor:q-order}{{8}{211}} \citation{ols_zame} \citation{rab_umz} \citation{89} \citation{krusam} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}$*$-Wildness of $*$-algebras}{212}} \newlabel{sec:3.1.2}{{3.1.2}{212}} \newlabel{th_o}{{52}{213}} \citation{117} \newlabel{th_t}{{53}{214}} \newlabel{def:14}{{14}{214}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.3}$*$-Wild algebras generated by orthogonal projections and idempotents}{214}} \newlabel{sec:3.1.3}{{3.1.3}{214}} \newlabel{th:anti-wild}{{55}{215}} \citation{krusam} \newlabel{th_f}{{57}{216}} \citation{112} \citation{113} \newlabel{th_fv}{{58}{219}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.4}$*$-Wild semilinear relations}{221}} \newlabel{sec:3.1.4}{{3.1.4}{221}} \newlabel{poly}{{3.1}{221}} \newlabel{pro:wild1}{{67}{221}} \newlabel{pro:wild2}{{68}{222}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.5}$*$-Wild quadratic and cubic relations}{222}} \newlabel{sec:3.1.5}{{3.1.5}{222}} \newlabel{quadr1}{{60}{223}} \newlabel{cub}{{3.3}{223}} \newlabel{tri}{{3.4}{224}} \newlabel{sis}{{3.5}{225}} \newlabel{th:cub1}{{61}{226}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.6}$*$-Wild groups. Periodic groups are not $*$-wild}{227}} \newlabel{sec:3.1.6}{{3.1.6}{227}} \newlabel{pr:wildgroups}{{71}{227}} \citation{kiril} \citation{olsh} \citation{adjan_book} \citation{ern} \newlabel{th:kal}{{62}{229}} \@writefile{toc}{\contentsline {section}{\numberline {3.2}On the complexity of the description of classes of non-self-adjoint operators}{229}} \newlabel{sec:3.2}{{3.2}{229}} \newlabel{rel:pxx}{{3.6}{230}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2.1}Classes of non-self-adjoint operators singled\penalty -\@M out by a quadratic or a cubic relation}{230}} \newlabel{sec:3.2.1}{{3.2.1}{230}} \newlabel{cond}{{3.7}{231}} \newlabel{polynom2}{{3.8}{231}} \newlabel{quadr2}{{63}{231}} \citation{91} \citation{halm2} \newlabel{qpline}{{3.9}{232}} \newlabel{qupline}{{3.10}{232}} \newlabel{a2b}{{3.11}{233}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2.2}Partial isometries, weakly centered operators and algebraic operators}{234}} \newlabel{sec:3.2.2}{{3.2.2}{234}} \citation{besp_mfat} \newlabel{th:wcpi}{{67}{235}} \citation{wog} \newlabel{cor7}{{73}{236}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2.3}Hyponormal operators and pairs of commuting completely non-unitary isometries}{236}} \newlabel{sec:3.2.3}{{3.2.3}{236}} \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}{238}} \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 {chapter}{Bibliography}{243}} \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} \@writefile{toc}{\contentsline {chapter}{Index}{259}}
Simpan