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 σa(T) of the Weyl essential approximate-point spectrum σwa(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.
AIENA P, J GUILLEN, P PENA (2008). PROPERTY (w) FOR PERTURBATIONS OF POLAROID OPERATORS. LINEAR ALGEBRA AND ITS APPLICATIONS, 428(8-9), 1791-1802 [10.1016/j.laa.2007.10.022].
PROPERTY (w) FOR PERTURBATIONS OF POLAROID OPERATORS
AIENA, Pietro;
2008-01-01
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 σa(T) of the Weyl essential approximate-point spectrum σwa(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.File | Dimensione | Formato | |
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