\(B\)-Fredholm and spectral properties for multipliers in Banach algebras
type: Item
instance of: scholarly article
title: \(B\)-Fredholm and spectral properties for multipliers in Banach algebras
zbMATH Open document ID: 1123.47031
DOI: 10.1007/BF02874778
author: A. Arroud
author: M. Berkani
publication date: 2007-07-19T00:00:00Z
review text: The paper studies spectral and \(B\)-Fredholm properties of multipliers acting on semi-simple regular Tauberian commutative Banach algebras. It is shown that a multiplier is \(B\)-Fredholm if and only if it is semi \(B\)-Fredholm, and in this case the index of \(T\) is zero. Spectral mapping theorems for the Weyl and \(B\)-Weyl spectrum are proven, and it is shown that the Weyl theorem and the generalized Weyl theorem hold for multipliers. Finally, sufficient conditions are given for a multiplier to be the product of an invertible and an idempotent operator.
reviewed by: Birgit Jacob
Mathematics Subject Classification ID: 47B48
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 5173053
zbMATH Keywords: Banach algebras
zbMATH Keywords: multipliers
zbMATH Keywords: \(B\)-Fredholm operators
zbMATH Keywords: Weyl's theorem
zbMATH Keywords: generalized Weyl's theorem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02874778
OpenAlex ID: W2025291100
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 5173053