Abstract

A Banach space operator T B() is polaroid (left polaroid) if isolated points of the spectrum (resp. isolated points of the approximate point spectrum) of T are poles of the resolvent of T (resp. are such that (T I) has finite ascent d and (T I)^d+1 is closed). Necessary and sufficient conditions for operators T B() to satisfy generalized and a-generalized Browder and Weyl theorems are given. In the case of polaroid (resp. left polaroid) operators T, it is proved that T satisfies generalized Weyl’s theorem (resp. generalized a-Weyl’s theorem) if and only if T satisfies Weyl’s theorem (resp. a-Weyl’s theorem).