EXTENDED WEYL TYPE THEOREMS AND PERTURBATIONS

In [9], we introduced the properties (b) and (gb), which are analogous of Browder and generalised Browder theorems. In this paper we study the stability of properties (b) and (gb) under commutative perturbations by finite rank, compact and nilpotent operators. Among other results, we prove that if T is an operator acting on a Banach space and possesses property (b) and N is a nilpotent operator commuting with T, then T + N possesses property (b). The same result holds for property (gb) in the case of a-polaroid operators.