Amenable traces and Folner C*-algebras
Articles
Overview
published in
- EXPOSITIONES MATHEMATICAE Journal
publication date
- January 2014
start page
- 161
end page
- 177
issue
- 2
volume
- 32
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 0723-0869
Electronic International Standard Serial Number (EISSN)
- 1878-0792
abstract
- In the present article we review an approximation procedure for amenable traces on unital and separable C*-algebras acting on a Hilbert space in terms of Folner sequences of non-zero finite rank projections. We apply this method to improve spectral approximation results due to Arveson and Bedos. We also present an abstract characterization in terms of unital completely positive maps of unital separable C*-algebras admitting a non-degenerate representation which has a Folner sequence or, equivalently, an amenable trace. This is analogous to Voiculescu's abstract characterization of quasidiagonal C*-algebras. We define Folner C*-algebras as those unital separable C*-algebras that satisfy these equivalent conditions. Finally we also mention some permanence properties related to these algebras.
Classification
keywords
- c*-algebras; folner sequences; amenable groups; amenable trace; crossed products; tensor products