Maximal semidefinite invariant subspaces for J-dissipative operators

Abstract

We describe some sufficient conditions for a J-dissipative operator in a Krein space to have maximal semidefinite invariant subspaces. The semigroup properties of the restrictions of an operator to these subspaces are studied. Appl ications are given to the case when an operator admits matrix representation with respect to the canonical decomposition of the space and to some singular differential operators. The main conditions are given in the terms of the interpolation theory of Banach spaces.