A note on some group $C^*$-algebras which are quasi-directly finite

Details A note on some group $C^*$-algebras which are quasi-directly finite A note on some group $C^*$-algebras which are quasi-directly finite

2010-03-08

arxiv.org/abs/1003.1650v2

Mathematics

Operator Algebras

v1: 10 pages, preliminary version. v2: 9 pages. New references and expanded discussion of the connected case, correcting an er

Scientific paper

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 $C^*$-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.

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