The generalized sectorial decompositions of semi-sectorial operators

This paper considers the generalized sectorial decompositions of semi-sectorial operators and quasi-sectorial operators on the complex Hilbert space. Under an invariant subspace condition, a necessary and sufficient condition for the existence of the generalized sectorial decomposition of a semi-sectorial operator is given. The generalized sectorial decomposition of a quasi-sectorial operator is given without any conditions. Some sufficient conditions for a block upper triangular operator matrix to be a semi-sectorial operator or a quasi-sectorial operator are given.