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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Bochner-Schoenberg-Eberlein property for commutative Banach algebras, especially Fourier and Fourier-Stieltjes algebras


Authors: Eberhard Kaniuth and Ali Ülger
Journal: Trans. Amer. Math. Soc. 362 (2010), 4331-4356
MSC (2010): Primary 46J05, 43A30; Secondary 46J10, 22E15
Published electronically: March 5, 2010
MathSciNet review: 2608409
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Abstract: The classical Bochner-Schoenberg-Eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group $ G$ which arise as Fourier-Stieltjes transforms of elements of the measure algebra $ M(G)$ of $ G$. This has led to the study of the algebra of BSE-functions on the spectrum of an arbitrary commutative Banach algebra and of the concept of a BSE-algebra as introduced by Takahasi and Hatori. Since then BSE-algebras have been studied by several authors. In this paper we investigate BSE-algebras in the general context on the one hand and, on the other hand, we specialize to Fourier and Fourier-Stieltjes algebras of locally compact groups.


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Additional Information

Eberhard Kaniuth
Affiliation: Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany
Email: kaniuth@math.uni-paderborn.de

Ali Ülger
Affiliation: Department of Mathematics, Koc University, 34450 Sariyer, Istanbul, Turkey
Email: aulger@ku.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05060-9
PII: S 0002-9947(10)05060-9
Keywords: Commutative Banach algebra, multiplier algebra, BSE-function, BSE-algebra, second duals, uniform algebra, unitization, locally compact group, Fourier and Fourier-Stieltjes algebras, Lipschitz algebra
Received by editor(s): September 14, 2008
Received by editor(s) in revised form: January 12, 2009
Published electronically: March 5, 2010
Additional Notes: The first author was supported by the German Research Foundation
The second author was supported by the Turkish Academy of Sciences
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.