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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Eberhard Kaniuth; Ali Ülger
Journal: Trans. Amer. Math. Soc. 362 (2010), 4331-4356.
MSC (2010): Primary 46J05, 43A30; Secondary 46J10, 22E15
Posted: March 5, 2010
MathSciNet review: 2608409
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The classical Bochner-Schoenberg-Eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group which arise as Fourier-Stieltjes transforms of elements of the measure algebra of . 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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