On the Property (gw) |
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Authors: | Mohammed Amouch Mohammed Berkani |
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Affiliation: | (1) Department of Mathematics, Semlalia Science faculty, University Caddi Ayyad, Marrakech, Morocco;(2) Department of Mathematics, Science faculty of Oujda, University Mohammed I, Team EQUITOMI, SFO Laboratory MATSI, EST, Oujda, Morocco |
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Abstract: | In this note we introduce and study the property (gw), which extends property (w) introduced by Rakoc̆evic in [23]. We investigate the property (gw) in connection with Weyl type theorems. We show that if T is a bounded linear operator T acting on a Banach space X, then property (gw) holds for T if and only if property (w) holds for T and Π a (T) = E(T), where Π a (T) is the set of left poles of T and E(T) is the set of isolated eigenvalues of T. We also study the property (gw) for operators satisfying the single valued extension property (SVEP). Classes of operators are considered as illustrating examples. The second author was supported by Protars D11/16 and PGR- UMP. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). 47A53 47A10 47A11 |
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