Search results for " Weyl's theorems"

showing 2 items of 2 documents

Property (w) and perturbations

2007

A bounded linear operator T ∈ L(X) defined on a Banach space X satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T ) of the Weyl essential approximate spectrum σwa(T ) coincides with 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 bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T .

Discrete mathematicsPure mathematicsApproximation propertyLocalized SVEP Weyl's theorems Browder's theorems PropertyApplied MathematicsBanach spaceFinite-rank operatorCompact operatorStrictly singular operatorBounded operatorSettore MAT/05 - Analisi MatematicaBounded inverse theoremC0-semigroupAnalysisMathematics
researchProduct

Property (w) and perturbations II

2008

AbstractThis note is a continuation of a previous article [P. Aiena, M.T. Biondi, Property (w) and perturbations, J. Math. Anal. Appl. 336 (2007) 683–692] concerning the stability of property (w), a variant of Weyl's theorem, for a bounded operator T acting on a Banach space, under finite-dimensional perturbations K commuting with T. A counterexample shows that property (w) in general is not preserved under finite-dimensional perturbations commuting with T, also under the assumption that T is a-isoloid.

Weyl's theoremsLocalized SVEP Weyl's theorems Browder's theorems Property (w)Property (w)Applied MathematicsLocalized SVEPBrowder's theoremsAnalysis
researchProduct