A Unifying Approach to Weyl Type Theorems for Banach Space Operators |
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Authors: | Pietro Aiena Jesús R Guillén Pedro Peña |
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Institution: | 1. Dipartimento di Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, Palermo, Italy 2. Departamento de Matemáticas, Facultad de Ciencias, ULA, Mérida, Venezuela 3. Departamento de Física y Matemáticas, NURR, ULA, Trujillo, Venezuela
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Abstract: | Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T + K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of T + K, such that f is non constant on each of the components of its domain. |
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