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DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

Part of: Selfadjoint operator algebras Abstract harmonic analysis Locally compact groups and their algebras

Published online by Cambridge University Press:  17 December 2014

YEMON CHOI
YEMON CHOI*
Affiliation:
Department of Mathematics and Statistics, Fylde College, Lancaster University, Bailrigg, Lancaster, Lancashire LA1 4YF, United Kingdom e-mail: [email protected]
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Abstract

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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.

MSC classification

Primary: 22D15: Group algebras of locally compact groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 3 , September 2015 , pp. 693 - 707
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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