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The Bochner–Schoenberg–Eberlein Property and Spectral Synthesis for Certain Banach Algebra Products

Published online by Cambridge University Press:  20 November 2018

Eberhard Kaniuth
Eberhard Kaniuth*
Affiliation:
Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany e-mail: [email protected]
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Abstract

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Associated with two commutative Banach algebras $A$ and $B$ and a character $\theta $ of $B$ is a certain Banach algebra product $A\,{{\times }_{\theta }}\,B$, which is a splitting extension of $B$ by $A$. We investigate two topics for the algebra $A\,{{\times }_{\theta }}\,B$ in relation to the corresponding ones of $A$ and $B$. The first one is the Bochner–Schoenberg–Eberlein property and the algebra of Bochner–Schoenberg–Eberlein functions on the spectrum, whereas the second one concerns the wide range of spectral synthesis problems for $A\,{{\times }_{\theta }}\,B$.

Keywords

46J1046J2543A3043A45commutative Banach algebrasplitting extensionGelfand spectrumset of synthesisweak spectral setmultiplier algebraBSE-algebraBSE-function
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 4 , 01 August 2015 , pp. 827 - 847
Copyright
Copyright © Canadian Mathematical Society 2015

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