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Property (R) under Perturbations |
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| Authors: | Pietro Aiena Elvis Aponte Jesús R. Guillén Pedro Peña |
| Affiliation: | 1. Dipartimento di Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, Via delle Scienze, Ed. 8, 90128, Palermo, Italy 2. Departamento de Matemáticas, Facultád de Ciencias UCLAB, Barquisimeto, Venezuela 3. Departamento de Matemáticas, Facultad de Ciencias, ULA, Merida, Venezuela 4. Departamento de Física y Matemáticas, NURR, ULA, Trujillo, Venezuela |
| Abstract: | Property (R) holds for a bounded linear operator ${T in L(X)}$ , defined on a complex infinite dimensional Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points λ of the approximate point spectrum for which λI ? 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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