The Calkin image of algebras of singular integral operators
type: Item
instance of: scholarly article
title: The Calkin image of algebras of singular integral operators
zbMATH Open document ID: 0702.47014
DOI: 10.1007/BF01196881
author: Steffen Roch
author: B. Silbermann
published in: Integral Equations and Operator Theory
publication date: 1989-01-01T00:00:00Z
review text: Let \({\mathcal A}\) be a Banach algebra of singular integral operators in \(L_ p(\Gamma,W)\) with piecewise continuous coefficient on the curves \(\Gamma\) with corners and intersections, W a Khvedelidse weight. The authors give the description of the image \({\mathcal A}^{\pi}\) in the Calkin algebra of the Banach algebra \({\mathcal A}\). Another very interesting result is that the algebra \({\mathcal A}^{\pi}\) remains invariant if the curve \(\Gamma\) is replaced by another curve \(\Gamma '\) being only homeomorphic to \(\Gamma\) and if the weight W is replaced by any other Khvedelidse weight. The authors discuss some applications of the main results so as symbol calculus, norm estimation, algebras with Carleman shift and with conjugation.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 46H35
zbMATH DE Number: 4151161
zbMATH Keywords: Banach algebra of singular integral operators
zbMATH Keywords: Khvedelidse weight
zbMATH Keywords: Calkin algebra
zbMATH Keywords: symbol calculus
zbMATH Keywords: norm estimation
zbMATH Keywords: algebras with Carleman shift
reviewed by: Vladimir Rabinovich
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196881
OpenAlex ID: W2053058395
description: scientific article; zbMATH DE number 4151161