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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite-dimensional right ideals in some algebras
associated with a locally compact group


Author: M. Filali
Journal: Proc. Amer. Math. Soc. 127 (1999), 1729-1734
MSC (1991): Primary 43A10, 22A15
Published electronically: February 11, 1999
MathSciNet review: 1473666
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Abstract: Let $G$ be a discrete group, a commutative discrete cancellative semigroup or a locally compact abelian group. Let $UC(G)$ be the space of bounded, uniformly continuous, complex-valued functions on $G.$ With an Arens-type product, the conjugate $UC(G)^{*}$ becomes a Banach algebra. We prove, that unlike left ideals, finite-dimensional right ideals exist in $UC(G)^{*}$ if and only if $G$ is compact.


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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: http://dx.doi.org/10.1090/S0002-9939-99-04631-6
PII: S 0002-9939(99)04631-6
Keywords: Locally compact group, uniformly continuous function, compactification, Borel measure, finite-dimensional right ideal
Received by editor(s): January 17, 1997
Received by editor(s) in revised form: September 11, 1997
Published electronically: February 11, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society