Amenable traces and Følner C∗-algebras Articles uri icon

publication date

  • January 2014

start page

  • 161

end page

  • 177

issue

  • 2

volume

  • 32

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 andseparable C∗-algebras acting on a Hilbert space in terms of Følner sequences of non-zero finite rankprojections. We apply this method to improve spectral approximation results due to Arveson andB´edos. We also present an abstract characterization in terms of unital completely positive maps ofunital separable C∗-algebras admitting a non-degenerate representation which has a Følner sequenceor, equivalently, an amenable trace. This is analogous to Voiculescu's abstract characterization ofquasidiagonal C∗-algebras. We define Følner C∗-algebras as those unital separable C∗-algebras thatsatisfy these equivalent conditions. Finally we also mention some permanence properties related tothese algebras.

keywords

  • c-algebras; folner sequences; amenable groups; amenable trace; crossed products; tensor products