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DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

Published online by Cambridge University Press:  17 December 2014

YEMON CHOI
Affiliation:
Department of Mathematics and Statistics, Fylde College, Lancaster University, Bailrigg, Lancaster, Lancashire LA1 4YF, United Kingdom e-mail: y.choi1@lancaster.ac.uk
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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 L1(G) is not directly finite when G is the affine group of either the real or complex line.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

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