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.
Aiena, P., Guillen, J., Pena, P. (2014). Property (gb) through local spectral theory. MATHEMATICAL PROCEEDINGS OF THE ROYAL IRISH ACADEMY, 114(114A (1)), 1-15 [doi:10:3318/PRIA.2014.114.01].
Property (gb) through local spectral theory
AIENA, Pietro;
2014-01-01
Abstract
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.
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