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
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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