On property (gw1)

Year 2014, Volume: 43 Issue: 4, 603 - 611, 01.08.2014

M. H. M. Rashid

Abstract

In this note we introduce and study the property (gw1), which extend
property (gw) introduced by Amouch and Berkani in [7]. We investigate the property (gw1) in connection with Weyl type theorems, and
establish for abounded linear operator defined on a Banach space the
sufficient and necessary conditions for which property (gw1) holds. We
also study the property (gw1) for operators satisfying the single valued extension property (SVEP). Classes of operators are considered as
illustrating examples.

Keywords

Generalized Weyl’s theorem, Generalized a-Weyl’s theorem, Property (gw1), Property (gw), Polaroid operators, Perturbation Theory

References

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