On Property (Baw1)

Neeru Kashyap

Abstract: This paper introduces the notion of property (Baw1), which is an extension of the property (Baw) defined and studied in [14]. We establish for a bounded linear operator defined on a Banach space the necessary and sufficient conditions for which the property (Baw1) holds. We discuss the property (Baw1) for operators satisfying the single valued extension property (SVEP).Certain conditions are explored on Hilbert space operators T and S so that T?S obeys the property (Baw1).We also study the preservation of the property (Baw) under perturbations by finite rank and nilpotent operators.

Keywords: Weyl's theorem, Generalized Weyl's theorem, Generalized Browder's theorem, SVEP, Property (Baw1), Property (Baw), Finitely polaroid operators