Generalized Drazin-type spectra of Operator matrices

Abstract

In this paper, we investigate the limit points set of surjective and approximate point spectra of upper triangular operator matrices M C = µ A C 0 B ¶. We prove that σ * (M C) ∪ W = σ * (A) ∪ σ * (B) where W is the union of certain holes in σ * (M C), which happen to be subsets of σ lgD (B) ∩ σ rgD (A), σ * ∈ {σ lgD , σ rgD } are the limit points set of surjective and approximate point spectra. Furthermore, several sufficient conditions for σ * (M C) = σ * (A) ∪ σ * (B) holds for every C ∈ B(Y, X) are given.