Hilbert C*-modules from group actions: beyond the finite orbits case

• Autorzy: Michael Frank , Vladimir Manuilov , Evgenij Troitsky
• Języki publikacji: EN

Abstrakty

EN

Continuous actions of topological groups on compact Hausdorff spaces X are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging allows one to derive a C*-valued inner product and a Hilbert C*-module which serve as an environment to describe characteristics of the group action. For Lyapunov stable actions the derived invariant mean $M(ϕ_{x})$ is continuous on X for any ϕ ∈ C(X), and the induced C*-valued inner product corresponds to a conditional expectation from C(X) onto the fixed-point algebra of the action defined by averaging on orbits. In the case of self-duality of the Hilbert C*-module all orbits are shown to have the same cardinality. Stable actions on compact metric spaces give rise to C*-reflexive Hilbert C*-modules. The same is true if the cardinality of finite orbits is uniformly bounded and the number of closures of infinite orbits is finite. A number of examples illustrate typical situations appearing beyond the classified cases.

Kategorie tematyczne

• 54H20: Topological dynamics
• 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
• 46L08: C * -modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 2
• Strony: 131-148

Daty

wydano

2010

Twórcy

autor

Michael Frank

• FB IMN, HTWK Leipzig, Postfach 301166, D-04251 Leipzig, Germany

autor

Vladimir Manuilov

• Department of Mechanics and Mathematics, Moscow State University, 119991 GSP-1 Moscow, Russia
• Harbin Institute of Technology, Harbin, P.R. China

autor

Evgenij Troitsky

• Department of Mechanics and Mathematics, Moscow State University, 119991 GSP-1 Moscow, Russia

Identyfikatory

DOI

10.4064/sm200-2-2