On certain products of Banach algebras with applications to harmonic analysis

Mehdi Sangani Monfared¹

¹ Department of Mathematics and Statistics University of Windsor Windsor, ON, N9B 3P4, Canada

Studia Mathematica, Tome 178 (2007) no. 3, pp. 277-294

Résumé

Given Banach algebras $A$ and $B$ with spectrum $\sigma (B)\ne \emptyset$, and given $\theta \in \sigma (B)$, we define a product $A\mathbin{\times_{\theta}} B$, which is a strongly splitting Banach algebra extension of $B$ by $A$. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming $B$ to be a Banach algebra in $\mathcal{C}_0(X)$ whose spectrum can be identified with $X$, we apply our results to harmonic analysis, and study the question of spectral synthesis, and primary ideals.

Détail

DOI : 10.4064/sm178-3-4

Keywords: given banach algebras spectrum sigma emptyset given theta sigma define product mathbin times theta which strongly splitting banach algebra extension nbsp obtain characterizations bounded approximate identities spectrum topological center minimal idempotents study ideal structure these products assuming banach algebra mathcal whose spectrum identified nbsp apply results harmonic analysis study question spectral synthesis primary ideals