Variations on Weyl type theorems

Abstract

In this paper we introduce and study two new properties (Bb) and (Bab) in connection with Weyl type theorems. It is shown that if T is a bounded linear operator acting on a Banach space X, then property (Bb) holds for T if and only if generalized Browder's theorem holds for T and π(T) = π 0 (T), where π(T) (resp., π 0 (T)) is the set of poles of resolvent of T (resp., the set of poles of resolvent of T of finite rank). A similar type of result has been obtained for property (Bab).