Finite-dimensional left ideals in some algebras

associated with a locally compact group

Author:
M. Filali

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2325-2333

MSC (1991):
Primary 43A10, 22D15

Published electronically:
April 9, 1999

MathSciNet review:
1487366

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a locally compact group, let be its group algebra, let be its usual measure algebra, let be the second dual of with an Arens product, and let be the conjugate of the space of bounded, left uniformly continuous, complex-valued functions on with an Arens-type product. We find all the finite-dimensional left ideals of these algebras. We deduce that such ideals exist in and if and only if is compact, and in (except those generated by right annihilators of ) and if and only if is amenable.

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Additional Information

**M. Filali**

Affiliation:
Department of Mathematical Sciences, University of Oulu, SF 90570 Finland

Email:
mfilali@cc.oulu.fi

DOI:
https://doi.org/10.1090/S0002-9939-99-04793-0

Keywords:
Locally compact group,
Arens product,
representation,
amenable,
$U$-invariant,
finite-dimensional left ideal

Received by editor(s):
October 28, 1997

Published electronically:
April 9, 1999

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1999
American Mathematical Society