On the continuity of the spectrum in certain Banach algebras

Israel Feldman, Naum Krupnik

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Abstract

In this paper we describe some classes of linear operators T ∈ L(H) (mainly Toeplitz, Wiener-Hopf and singular integral) on a Hubert spaces H such that the spectrum σ(T,L(H)) is continuous at the points T from these classes. We also describe some subalgebras A of the algebras à for which the spectrum σ(χ, Ã) becomes continuous at the points χ when σ(χ, Ã) is restricted to the subalgebra A. In particular, we show that the spectrum σ(χ, Ã) is continuous in Banach algebras à with polynomial identities. Examples of such algebras are given.

Original languageEnglish
Pages (from-to)284-301
Number of pages18
JournalIntegral Equations and Operator Theory
Volume38
Issue number3
DOIs
StatePublished - 2000

Bibliographical note

Funding Information:
iThis research was partially supported by the Israel Science Fmmdation founded by tile Israel Academy of Sciences arid Humanit.ies.

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