On existence of maximal semidefinite invariant subspaces for $J$-dissipative operators
Sergey Grigor'evich Pyatkov · arXiv (Cornell University) · 2010
We describe necessary and 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. Applications are given to the case when an operator admits matrix representation with respect to the canonical decomposition of the space. The main conditions are given in the terms of the interpolation theory of Banach spaces.