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 M C = ( A C 0 B ) {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.