The residual spectrum and the continuous spectrum of upper triangular operator matrices

Abstract

Let H and K be separable infinite dimensional Hilbert spaces. We denote by MC the 2x2 upper triangular operator matrix acting on H ? K of the form MC = (A C/0 B ). For given operators A ? B(H) and B ? B(K), the sets C?B?(K,H) ?r(MC) and C?B?(K,H) ?c(MC) are characterized, where ?r(?) and ?c(?) denote the residual spectrum and the continuous spectrum, respectively