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RESEARCH PRODUCT
Generalized Browder’s Theorem and SVEP
Orlando GarciaPietro Aienasubject
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 eigenvectorsResolventMathematicsdescription
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 subsets of \({\mathbb{C}}\). In the last part we give a general framework for which generalized Weyl’s theorem follows for several classes of operators.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-07-01 | Mediterranean Journal of Mathematics |