Andrey BONDARENKO
Kyiv National Taras Shevchenko University,
60 Volodymyrs'ka Str.,
Kyiv-33, 01033  UKRAINE
E-mail: bondarenkoa@ukr.net

Description of the set of anti-Fock representations for *-algebras connected with an unimodal mappings

Abstract:
In papers [1, 2] a C*-algebra connected to a simple non-bijective dynamical system was constructed. Attempting to construct C*-algebra in more general case we start, as in those papers, with description of the set of representations.  The method of description of anti-Fock representations of the relation XX*=f(X*X) for
continuous unimodal mapping  f was devised.

References:

1. Popovych S.V. and Maistrenko T.Yu., $C^*$-algebras, associated with $\mathcal{F}_{2^n}$ unimodal dynamical systems, Ukrainian Math. J., 2001, V.53, N 7, 929-938.
2. Bondarenko A.V., Popovych S.V., $C^*$-Algebras Associated with  $\mathcal{F}_{2^n}$ Zero Schwarzian Unimodal Mappings, Proceedings of Institute of Mathematics of NAS of Ukraine, 2002, V.43, Part 2, 425-431.