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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
The second author was supported by Protars D11/16 and PGR- UMP.
Rights and permissions
About this article
Cite this article
Amouch, M., Berkani, M. On the Property (gw). MedJM 5, 371–378 (2008). https://doi.org/10.1007/s00009-008-0156-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-008-0156-z