Search results for "Local spectral theory"
showing 4 items of 4 documents
Some characterizations of operators satisfying a-Browder's theorem
2005
Abstract We characterize the bounded linear operators T defined on Banach spaces satisfying a-Browder's theorem, or a-Weyl's theorem, by means of the discontinuity of some maps defined on certain subsets of C . Several other characterizations are given in terms of localized SVEP, as well as by means of the quasi-nilpotent part, the hyper-kernel or the analytic core of λ I − T .
On the spectral properties of some classes of operators
2010
This article concerns the spectral properties of some classes of operators defined by means some inequelities
Weyl's and Browder's theorems through the quasi-nilpotent part
2006
Weyl and Browder type theorems are characterized by means the quasi-nilpotent part
Property (gb) through local spectral theory
2014
Property (gb) for a bounded linear operator T on a Banach space X means that the points c of the approximate point spectrum for which c I-T is upper semi B-Weyl are exactly the poles of the resolvent. In this paper we shall give several characterizations of property (gb). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gb) holds for large classes of operators and prove the stability of property (gb) under some commuting perturbations.