SPECTRAL DECOMPOSITION OF SOME NONSELFADJOINT BLOCK OPERATOR MATRICES

Abstract

In this note we study spectral properties of a block operator matrix e A (see (1.1) below), where A and −D are m-accretive, and B, D are bounded operators. Under an additional assumption, the spectrum of e A consists of one part in the extended right and one part in the left half plane, and the corresponding spectral subspaces allow representations by means of angular operators. If the part of the spectrum of e A in the right half plane is discrete, a half range completeness statement follows. As an essential tool the quadratic numerical range of a block operator matrix is introduced.