Almost invariant half-spaces for operators on Hilbert space. II: operator matrices

This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier proofs of the main results in [1] and [13]. In the present paper we discuss consequences of the above-mentioned results for the matricial structure of operators on Hilbert space.