Continuity of spectrum and approximate point spectrum on operator matrices

Let X and Y be given Banach spaces. For A ∈ B ( X ) , B ∈ B ( Y ) and C ∈ B ( Y , X ) , let M C be the operator defined on X ⊕ Y by M C = [ A C 0 B ] . In this paper we give conditions for continuity of τ at M C through continuity of τ at A and B, where τ can be equal to the spectrum or approximate point spectrum.