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
- Trans. Amer. Math. Soc. 362 (2010), 4331-4356
- DOI: https://doi.org/10.1090/S0002-9947-10-05060-9
- Published electronically: March 5, 2010
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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.References
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Bibliographic 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
- 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 - © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 4331-4356
- MSC (2010): Primary 46J05, 43A30; Secondary 46J10, 22E15
- DOI: https://doi.org/10.1090/S0002-9947-10-05060-9
- MathSciNet review: 2608409