Abstract. In [AMB] we introduced and studied property $(gw),$ which is an extension to the context of B-Fredholm theory, of the property $(w)$ introduced by Rakočević in [RA1]. In this paper we continue the study of property $(gw)$ and we consider its preservation under perturbations by finite rank and nilpotent operators.

AMS Subject Classification (1991): 47A53, 47A10, 47A11

Keyword(s): B, -Fredholm operator, Weyl's theorem, generalized Weyl's theorem, a, -Weyl's theorem, a, generalized-Weyl's theorem, (gw), property

Received June 21, 2007, and in final form January 31, 2008. (Registered under 6045/2009.)