Let A be a commutative semisimple Banach algebra, Δ(A) its Gelfand spectrum, T a multiplier on A and T̂ its Gelfand transform. We study the following problems. (a) When is δ(T) = inf{|T̂(f)|: f ∈ Δ(A), T̂(f) ≠ 0} > 0? (b) When is the range T(A) of T closed in A and does it have a bounded approximate identity? (c) How to characterize the idempotent multipliers in terms of subsets of Δ(A)?
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-1-5,
author = {A. \"Ulger},
title = {Multipliers with closed range on commutative semisimple Banach algebras},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {59-80},
zbl = {1042.47026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-1-5}
}
A. Ülger. Multipliers with closed range on commutative semisimple Banach algebras. Studia Mathematica, Tome 151 (2002) pp. 59-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-1-5/