Mediterranean Journal of Mathematics

, Volume 5, Issue 3, pp 371–378 | Cite as

On the Property (gw)



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.

Mathematics Subject Classification (2000).

47A53 47A10 47A11 


B-Fredholm operator Weyl’s theorem generalized Weyl’s theorem a-Weyl’s theorem generalized a-Weyl’s theorem property (gw


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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Semlalia Science facultyUniversity Caddi AyyadMarrakechMorocco
  2. 2.Department of Mathematics, Science faculty of OujdaUniversity Mohammed I, Team EQUITOMI, SFO Laboratory MATSI, ESTOujdaMorocco

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