On the existence of maximal semidefinite invariant subspaces for $J$-dissipative operators

For a certain class of operators we present some necessary and sufficient conditions for a $J$-dissipative operator in a Kreǐn space to have maximal semidefinite invariant subspaces. We investigate the semigroup properties of restrictions of the operator to these invariant subspaces. These results are applied to the case when the operator admits a matrix representation with respect to the canonical decomposition of the space. The main conditions are formulated in terms of interpolation theory for Banach spaces.
Bibliography: 25 titles.