The point, residual and continuous spectrum of an upper triangular operator matrix ?

摘要

In this paper, for given operators A ∈ B(H) and B ∈ B(K), we completely describe the set of all C ∈ B(K, H) such that M_C is injective, R(M_C) is not dense in H?K, respectively and describe residual and continuous spectrum of the upper triangular operator matrix M_C.