In this article we study the property (gab) for a bounded linear operator T ∈ L(X) on a Banach space X which is a stronger variant of Browder’s theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations.
Aiena, P., Triolo, S. (2015). Property (gab) through localized SVEP. MOROCCAN JOURNAL OF PURE AND APPLIED ANALYSIS, 1(2), 91-107 [10.7603/s40956-015-0007-4].
Property (gab) through localized SVEP
AIENA, Pietro
;TRIOLO, Salvatore
2015-01-01
Abstract
In this article we study the property (gab) for a bounded linear operator T ∈ L(X) on a Banach space X which is a stronger variant of Browder’s theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations.
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