Generalized Weyl's theorem and quasi-affiniy.

A bounded operator T in L(X) acting on a Banach space X is said to satisfy generalized Weyl's theorem if the complement in the spectrum of the B-Weyl spectrum is the set of all eigenvalues which are isolated points of the spectrum. In this paper we prove that generalized Weyl's theorem holds for several classes of operators, extending previous results obtained in [24] and [15]. We also consider the preservation of generalized Weyl's theorem between two operators T in L(X), S in L(Y ) in the case that these are intertwined by a quasi-affinity A in L(X; Y ), or in the more general case that T and S are asymptotically intertwined by A.