On certain products of Banach algebras with applications to harmonic analysis

Tom 178 / 2007

Mehdi Sangani Monfared Studia Mathematica 178 (2007), 277-294 MSC: Primary 46H20, 46H10, 46J20, 43A45; Secondary 46J10, 43A30. DOI: 10.4064/sm178-3-4


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.


  • Mehdi Sangani MonfaredDepartment of Mathematics and Statistics
    University of Windsor
    Windsor, ON, N9B 3P4, Canada

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