A note on some group $C^*$-algebras which are quasi-directly finite
Operator Algebras
2010-06-08 v2 Functional Analysis
Abstract
An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property; in this note, we collate some analogous results for the group -algebras of more general locally compact groups. Partial motivation comes from earlier work of the author on the phenomenon of empty residual spectrum for convolution operators.
Keywords
Cite
@article{arxiv.1003.1650,
title = {A note on some group $C^*$-algebras which are quasi-directly finite},
author = {Yemon Choi},
journal= {arXiv preprint arXiv:1003.1650},
year = {2010}
}
Comments
v1: 10 pages, preliminary version. v2: 9 pages. New references and expanded discussion of the connected case, correcting an error in the previous version; other minor improvements throughout