Dunford's property \((C)\) and Weyl's theorems.
type: Item
instance of: scholarly article
title: Dunford's property \((C)\) and Weyl's theorems.
zbMATH Open document ID: 1034.47003
DOI: 10.1007/BF01255564
published in: Integral Equations and Operator Theory
publication date: 2002-01-01T00:00:00Z
review text: A (bounded linear) operator \(T\) on a Banach space \(X\) satisfies Weyl's theorem if its Weyl spectrum coincides with the complement in the spectrum of the isolated point spectrum. An operator \(T\) on \(X\) satisfies the single valued extension property if each complex number has a neighbourhood on which \(f=0\) is the only \(X\)-valued analytic function satisfying \((T-\lambda)f(\lambda)=0\). Dunford's property (C) is similar but stronger. Conditions are given relating property (C) with Weyl's theorem for operators which intertwine in the sense that \(AY=YB\). Weyl's theorem is proved for various classes of operators including \(M\)-hyponormal operators. Moreover, the Weyl spectra of these operators satisfy the spectral mapping theorem with respect to functions analytic in a neighbourhood of the spectrum.
reviewed by: Alan J. Pryde
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A11
zbMATH DE Number: 1802507
zbMATH Keywords: Weyl theorem
zbMATH Keywords: Weyl spectrum
zbMATH Keywords: Dunford property (C)
zbMATH Keywords: spectral mapping theorem
author: B. P. Duggal
author: Slaviša Djordjevic
MaRDI profile type: Publication
cites work: Quasi-similar \(p\)-hyponormal operators
cites work: \(p\)-hyponormal operators satisfy Bishop's condition \({\beta}\)
cites work: Q3828563
cites work: Q4139233
cites work: The single valued extension property on a Banach space
cites work: Q3994350
cites work: Another note on Weyl’s theorem
cites work: Q3697643
cites work: Weyl's theorem for \(f(T)\) when \(T\) is a dominant operator
cites work: Isolated spectral points
cites work: Operators with finite ascent
cites work: Asymptotic intertwining and spectral inclusions on Banach spaces
cites work: Local spectral theory and spectral inclusions
cites work: Essential spectra through local spectral theory
cites work: Generalisation de la decomposition de kato aux opérateurs paranormaux et spectraux
cites work: On the Weyl spectrum. II
cites work: Q4939438
cites work: Spectral structure and subdecomposability of $p$-hyponormal operators
cites work: Q3934997
full work available at URL: https://doi.org/10.1007/bf01255564
OpenAlex ID: W2007879126
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description: scientific article; zbMATH DE number 1802507