Limit points for descent spectrum of operator matrices

Abstract

Abstract In this paper, we investigate the limit points set of descent spectrum of upper triangular operator matrices MC=(AC0B) {M_C} = \left( {\matrix{A \hfill & C \hfill \cr 0 \hfill & B \hfill \cr } } \right) . We prove that acc(σdes(MC)) ∪ Waccσdes = acc(σdes(A)) ∪ acc(σdes(B)) where Waccσdes is the union of certain holes in acc(σdes(MC)), which happen to be subsets of acc(σasc(B)) ∩ acc(σdes(A)). Furthermore, several sufficient conditions for acc(σdes(MC)) = acc(σdes(A)) ∪ acc(σdes(B)) holds for every C ∈ ℬ(Y, X) are given.