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The Bochner–Schoenberg–Eberlein Property and Spectral Synthesis for Certain Banach Algebra Products
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- Journal:
- Canadian Journal of Mathematics / Volume 67 / Issue 4 / 01 August 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 827-847
- Print publication:
- 01 August 2015
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- Article
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- You have access
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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 $A\,{{\times }_{\theta }}\,B$.
