On sectorial block operator matrices

The paper deals with linear operators in the Hilbert space $H_1\oplus H_2$ defined by matrices with, in general, unbounded entries. Criterions for such operators to be sectorial with the vertex at the origin are obtained, parametrization of all its m-accretive and m-sectorial extensions and a description of root subspaces of such extensions by means of the transfer function (Schur complement) and its derivatives are given. Analytical properties of the Friedrichs extensions of the transfer function of a sectorial block operator matrix are established.