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On certain products of Banach algebras with applications to harmonic analysis

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Monfared M.

Studia Mathematica

2007

tom 178

nr 3

277-294

Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product $A ×_{θ} B$, 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 𝓒₀(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.

Ograniczanie wyników

1 Studia Mathematica

1 Monfared M.

1 2007

Wyniki wyszukiwania

On certain products of Banach algebras with applications to harmonic analysis