Weak essential spectra of multiplication operators on spaces of bounded linear operators
type: Item
instance of: scholarly article
title: Weak essential spectra of multiplication operators on spaces of bounded linear operators
zbMATH Open document ID: 0805.47002
DOI: 10.1007/BF01459786
author: Eero Saksman
author: Hans-Olav Tylli
published in: Mathematische Annalen
publication date: 1994-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165211
review text: Let \(E\) be a (complex) Banach space and consider the multiplication operator \(A\land B: S\mapsto BSA\) on \(L(E)\) for \(A,B\in L(E)\). The spectrum of \(A\land B\in L(L(\ell^ p))\) modulo \(W(L(\ell^ p))\) is determined. In addition, a general spectral inclusion formula is established which enables one to compute the spectrum of \(A\land B\) modulo \(W(L(E))\) if \(E'\) has the Dunford-Pettis property. The distance of \(A\land B\) to the weakly compact operators on \(L(\ell^ p)\) is calculated. Similar results hold for the restriction of \(A\land B\) to Banach ideals \(I(E)\) of \(L(E)\). This study complements several previous results concerning the spectrum and the essential spectrum of \(A\land B\).
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47B99
zbMATH DE Number: 683146
zbMATH Keywords: multiplication operator
zbMATH Keywords: spectral inclusion formula
zbMATH Keywords: Dunford-Pettis property
zbMATH Keywords: weakly compact operators
zbMATH Keywords: Banach ideals
MaRDI profile type: Publication
Wikidata QID: Q109553852
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description: scientific article; zbMATH DE number 683146