Invertibility in groupoid C*-algebras
Operator Algebras
2013-02-08 v1
Abstract
Given a second-countable, Hausdorff, \'etale, amenable groupoid G with compact unit space, we show that an element a in C*(G) is invertible if and only if \lambda_x(a) is invertible for every x in the unit space of G, where \lambda_x refers to the "regular representation" of C*(G) on l_2(G_x). We also prove that, for every a in C*(G), there exists some x in G^{(0)} such that ||a|| = ||\lambda_x(a)||.
Keywords
Cite
@article{arxiv.1302.1728,
title = {Invertibility in groupoid C*-algebras},
author = {Ruy Exel},
journal= {arXiv preprint arXiv:1302.1728},
year = {2013}
}
Comments
8 pages