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

S. G. Pyatkov

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

Functional Analysis 2010-07-26 v1

Authors: S. G. Pyatkov

Abstract

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.

Keywords

operator theory on banach spaces invariant subspace theory banach space

Cite

@article{arxiv.1007.4131,
  title  = {On existence of maximal semidefinite invariant subspaces for $J$-dissipative operators},
  author = {S. G. Pyatkov},
  journal= {arXiv preprint arXiv:1007.4131},
  year   = {2010}
}

Comments

22 pages

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