Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product , 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-4,
author = {Mehdi Sangani Monfared},
title = {On certain products of Banach algebras with applications to harmonic analysis},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {277-294},
zbl = {1121.46041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-4}
}
Mehdi Sangani Monfared. On certain products of Banach algebras with applications to harmonic analysis. Studia Mathematica, Tome 178 (2007) pp. 277-294. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-4/