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On the essential spectrum of Banach-space operators

Published online by Cambridge University Press:  20 January 2009

Jörg Eschmeier
Jörg Eschmeier
Affiliation:
Fachbereich Mathematik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
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Abstract

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Let T and S be quasisimilar operators on a Banach space X. A well-known result of Herrero shows that each component of the essential spectrum of T meets the essential spectrum of S. Herrero used that, for an n-multicyclic operator, the components of the essential resolvent set with maximal negative index are simply connected. We give new and conceptually simpler proofs for both of Herrero's results based on the observation that on the essential resolvent set of T the section spaces of the sheaves

are complete nuclear spaces that are topologically dual to each other. Other concrete applications of this result are given.

Keywords

quasisimilarityessential spectrumcoherent sheavessheaf models
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 511 - 528
Copyright
Copyright © Edinburgh Mathematical Society 2000

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