Amenable traces and Følner C*-algebras

Pere Ara, Fernando Lledó

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

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 Følner sequences of non-zero finite rank projections. We apply this method to improve spectral approximation results due to Arveson and Bédos. 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 Følner sequence or, equivalently, an amenable trace. This is analogous to Voiculescu's abstract characterization of quasidiagonal C*-algebras. We define Følner C*-algebras as those unital separable C*-algebras that satisfy these equivalent conditions. Finally we also mention some permanence properties related to these algebras. © 2013 Elsevier Ltd.
Original languageEnglish
Pages (from-to)161-177
JournalExpositiones Mathematicae
Volume32
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Amenable groups
  • Amenable trace
  • Crossed products
  • Følner sequences
  • Tensor products

Fingerprint Dive into the research topics of 'Amenable traces and Følner C<sup>*</sup>-algebras'. Together they form a unique fingerprint.

Cite this