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Amenable traces and Følner C*-algebras

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URI: https://hdl.handle.net/10016/23377
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2013.10.002
UXXI: AR/0000018015
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amenable_Lledo_EM_2014_ps.pdf (551.81 KB)
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2014
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Elsevier
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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 and Bédos. 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.
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C-algebras, Folner sequences, Amenable groups, Amenable trace, Crossed products, Tensor products
Bibliographic citation
Expositiones Mathematicae, 2014, v. 32, Issue 2, pp. 161-177
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