Multipliers with closed range on commutative semisimple Banach algebras
Volume 153 / 2002
Studia Mathematica 153 (2002), 59-80
MSC: Primary 47B48, 46J10, 43A22.
DOI: 10.4064/sm153-1-5
Abstract
Let $A$ be a commutative semisimple Banach algebra, ${\mit\Delta} (A)$ its Gelfand spectrum, $T$ a multiplier on $A$ and $\widehat{T}$ its Gelfand transform. We study the following problems. (a) When is $\delta (T)=\inf \{| \widehat{T}(f)|:f\in {\mit\Delta} (A)$, $\widehat{T}(f)\neq 0\}>0?$ (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 ${\mit\Delta} (A)?$
