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 .

AIENA P, BIONDI M T (2007). Property (w) and perturbations. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 336(1), 683-692 [10.1016/j.jmaa.2007.02.084].

Property (w) and perturbations

AIENA, Pietro;
2007-01-01

Abstract

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 .
Settore MAT/05 - Analisi Matematica
AIENA P, BIONDI M T (2007). Property (w) and perturbations. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 336(1), 683-692 [10.1016/j.jmaa.2007.02.084].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/15629
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