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

Kaniuth, Eberhard

Canadian journal of mathematics, Tome 67 (2015) no. 4, pp. 827-847

Résumé

Associated with two commutative Banach algebras $A$ and $B$ and a character $\theta $ of $B$ is acertain 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 $A\,{{\times }_{\theta }}\,B$ .

Détail

DOI : 10.4153/CJM-2014-028-4

Mots-clés : 46J10, 46J25, 43A30, 43A45, commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSE-algebra, BSE-function