Topological uniform descent and Weyl type theorem

Abstract

The generalized Weyl’s theorem holds for a Banach space operator T if and only if T or T ∗ has the single valued extension property in the complement of the Weyl spectrum (or B-Weyl spectrum) and T has topological uniform descent at all λ which are isolated eigenvalues of T. Also, we show that the generalized Weyl’s theorem holds for analytically paranormal operators.