Property (a B w) and Weyl Type Theorems

Abstract

In this paper, we introduces the property (a B w), a variant of generalized a-Weyl’s theorem for a bounded linear operator T on an infinite-dimensional Banach space \(\mathbb {X}\). We establish several sufficient and necessary conditions for which property (a B w) holds. Also, we prove that if \(T\in \mathbf {L(\mathbb {X})}\) satisfies property (a B w) then T satisfies property (B w). Certain conditions are explored on Hilbert space operators T and S so that T ⊕ S obeys property (a B w).