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

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

2010-07-23

arxiv.org/abs/1007.4131v1

Mathematics

Functional Analysis

22 pages

Scientific paper

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.

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