The approximation property and exactness of locally compact groups
Operator Algebras
2021-01-26 v4 Group Theory
Abstract
We extend a theorem of Haagerup and Kraus in the C*-algebra context: for a locally compact group with the approximation property (AP), the reduced C*-crossed product construction preserves the strong operator approximation property (SOAP). In particular their reduced group C*-algebras have the SOAP. Our method also solves another open problem: the AP implies exactness for general locally compact groups.
Keywords
Cite
@article{arxiv.1901.07430,
title = {The approximation property and exactness of locally compact groups},
author = {Yuhei Suzuki},
journal= {arXiv preprint arXiv:1901.07430},
year = {2021}
}
Comments
11 pages, minor revision, to appear in J. Math. Soc. Japan