Home > Research > Publications & Outputs > Directly finite algebras of pseudofunctions on ...

Electronic data

  • 1205.4354v4

    Rights statement: http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 57 (3), pp 693-707 2015, © 2015 Cambridge University Press.

    Accepted author manuscript, 155 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

  • 2014-05-12_gmj_acceptance

    Accepted author manuscript, 44.6 KB, PDF document

Links

Text available via DOI:

View graph of relations

Directly finite algebras of pseudofunctions on locally compact groups

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>09/2015
<mark>Journal</mark>Glasgow Mathematical Journal
Issue number3
Volume57
Number of pages15
Pages (from-to)693-707
Publication StatusPublished
Early online date17/12/14
<mark>Original language</mark>English

Abstract

An algebra $A$ is said to be directly finite if each left-invertible element
in the (conditional) unitization of $A$ is right invertible. We show that the reduced group $C^*$-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of $p$-pseudofunctions, showing that these algebras are directly finite if $G$ is amenable and unimodular, or unimodular with the Kunze--Stein property.

An exposition is also given of how existing results from the literature imply that $L^1(G)$ is not directly finite when $G$ is the affine group of either the real or complex line.

Bibliographic note

http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 57 (3), pp 693-707 2015, © 2015 Cambridge University Press.