Variations on Weyl type theorems

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 boundedlinear operator acting on a Banach space $X$, then property (Bb) holds for $T$ if andonly if generalized Browder's theorem holds for $T$ and $pi(T) =pi_0(T) $, where$pi(T)$ (resp., $pi_0(T)$) is the set of poles of resolvent of $T$ (resp., the set of polesof resolvent of $T$ of finite rank). A similar type of result has been obtained forproperty (Bab).