Property (R) holds for a bounded linear operator T defined on a complex Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points c of the approximate point spectrum such CI- T is upper semi-Browder. In this paper we consider the permanence of this property under quasi nilpotent, Riesz or algebraic perturbations commuting with T.
Aiena, P., Aponte, E., Guillen, J., Pena, P. (2013). Property (R) under perturbations. MEDITERRANEAN JOURNAL OF MATHEMATICS, 10(Volume: 10 Issue: 1), 367-382.
Property (R) under perturbations
AIENA, Pietro;
2013-01-01
Abstract
Property (R) holds for a bounded linear operator T defined on a complex Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points c of the approximate point spectrum such CI- T is upper semi-Browder. In this paper we consider the permanence of this property under quasi nilpotent, Riesz or algebraic perturbations commuting with T.
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