On certain products of Banach algebras with applications to harmonic analysis

• Autorzy: Mehdi Sangani Monfared
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 46J20: Ideals, maximal ideals, boundaries
• 46H10: Ideals and subalgebras
• 46J10: Banach algebras of continuous functions, function algebras
• 46H20: Structure, classification of topological algebras
• 43A45: Spectral synthesis on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 3
• Strony: 277-294

Daty

wydano

2007

Twórcy

autor

Mehdi Sangani Monfared

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

Identyfikatory

DOI

10.4064/sm178-3-4