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

Kaniuth, Eberhard; Ülger, Ali

doi:10.1090/S0002-9947-10-05060-9

The Bochner-Schoenberg-Eberlein property for commutative Banach algebras, especially Fourier and Fourier-Stieltjes algebras
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by Eberhard Kaniuth and Ali Ülger PDF

Trans. Amer. Math. Soc. 362 (2010), 4331-4356 Request permission

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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