# Property ( a B w ) and Weyl Type Theorems

Research paper by Mohammad H. M. Rashid

Indexed on: 21 Nov '17Published on: 01 Dec '17Published in: Acta Mathematica Vietnamica

#### 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).