On the continuity of the spectrum in certain Banach algebras

Israel Feldman; Naum Krupnik

doi:10.1007/bf01291715

On the continuity of the spectrum in certain Banach algebras

Israel Feldman, Naum Krupnik

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 Ã 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 Ã with polynomial identities. Examples of such algebras are given.

Original language	English
Pages (from-to)	284-301
Number of pages	18
Journal	Integral Equations and Operator Theory
Volume	38
Issue number	3
DOIs	https://doi.org/10.1007/bf01291715
State	Published - 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.

Funding

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

Funders	Funder number
Israel Science Fmmdation founded by tile Israel Academy of Sciences

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10.1007/bf01291715

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title = "On the continuity of the spectrum in certain Banach algebras",

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 {\~A} for which the spectrum σ(χ, {\~A}) becomes continuous at the points χ when σ(χ, {\~A}) is restricted to the subalgebra A. In particular, we show that the spectrum σ(χ, {\~A}) is continuous in Banach algebras {\~A} with polynomial identities. Examples of such algebras are given.",

author = "Israel Feldman and Naum Krupnik",

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AU - Feldman, Israel

AU - Krupnik, Naum

N1 - Funding Information: iThis research was partially supported by the Israel Science Fmmdation founded by tile Israel Academy of Sciences arid Humanit.ies.

PY - 2000

Y1 - 2000

N2 - 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 Ã 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 Ã with polynomial identities. Examples of such algebras are given.

AB - 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 Ã 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 Ã with polynomial identities. Examples of such algebras are given.

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

On the continuity of the spectrum in certain Banach algebras

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