Search results for " Weyl’s theorem"

showing 3 items of 3 documents

Some spectral mapping theorems through local spectral theory

2004

The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra. We also prove that ifT orT* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the caseT orT* has the single valued extension property, tof(T), wheref is an analytic function defined on an open disc containing the spectrum ofT. In the last part we improve a re…

Pure mathematicsSpectral theoryTransform theoryGeneral MathematicsSpectrum (functional analysis)Mathematical analysisExtension (predicate logic)Single valued extension property Weyl and semi-Browder operators spectral mapping theorems Weyl’s theoremFredholm theorySpectral linesymbols.namesakesymbolsSpectral theory of ordinary differential equationsAnalytic functionMathematicsRendiconti del Circolo Matematico di Palermo
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Property (w) for perturbations of polaroid operators

2008

Abstract A bounded linear operator T ∈ L ( X ) acting on a Banach space satisfies property ( w ) , a variant of Weyl’s theorem, if the complement in the approximate point spectrum σ a ( T ) of the Weyl essential approximate-point spectrum σ wa ( T ) is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property ( w ) for a polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T.

Unbounded operatorDiscrete mathematicsNumerical AnalysisPure mathematicsAlgebra and Number TheoryApproximation propertyProperty (w)Weyl’s theoremsFredholm operatorSpectrum (functional analysis)Banach spaceProperty (w) Weyl’s theorems Polaroid operatorsFinite-rank operatorOperator theoryBounded operatorPolaroid operatorsDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematicsLinear Algebra and its Applications
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Generalized Browder’s Theorem and SVEP

2007

A bounded operator \(T \in L(X), X\) a Banach space, is said to verify generalized Browder’s theorem if the set of all spectral points that do not belong to the B-Weyl’s spectrum coincides with the set of all poles of the resolvent of T, while T is said to verify generalized Weyl’s theorem if the set of all spectral points that do not belong to the B-Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues. In this article we characterize the bounded linear operators T satisfying generalized Browder’s theorem, or generalized Weyl’s theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(λI − T) as λ belongs to certain …

Unbounded operatorDiscrete mathematicsPure mathematicsGeneral MathematicsSpectrum (functional analysis)Banach spaceBounded operatorSettore MAT/05 - Analisi MatematicaBounded functionSVEP Fredholm theory generalized Weyl’s theorem and generalized Browder’s theoremMathematics::Representation TheoryBounded inverse theoremEigenvalues and eigenvectorsResolventMathematicsMediterranean Journal of Mathematics
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