On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity

Erik Bedos; Roberto Conti

On discrete twisted C-dynamical systems, Hilbert C-modules and regularity

Operator Algebras 2013-01-11 v4 Dynamical Systems Functional Analysis

Authors: Erik Bedos , Roberto Conti

Abstract

We first give an overview of the basic theory for discrete unital twisted C*-dynamical systems and their covariant representations on Hilbert C*-modules. After introducing the notion of equivariant representations of such systems and their product with covariant representations, we prove a kind of Fell absorption principle saying that the product of an induced regular equivariant representation with a covariant faithful representation is weakly equivalent to an induced regular covariant representation. This principle is the key to our main result, namely that a certain property, formally weaker than Exel's approximation property, ensures that the system is regular, i.e., the associated full and reduced C*-crossed products are canonically isomorphic.

Keywords

hilbert modules c*-algebras c*-algebra

Cite

@article{arxiv.1104.1731,
  title  = {On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity},
  author = {Erik Bedos and Roberto Conti},
  journal= {arXiv preprint arXiv:1104.1731},
  year   = {2013}
}

Comments

Final version, to appear in Muenster J. Math. A permanence result for the weak approximation property, some corollaries of it and two examples have been added to Section 5. Some side results in Section 4 have been removed and will be included in a subsequent paper. The Introduction has also been partly rewritten