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Maximal Semidefinite Invariant Subspaces for J-dissipative Operators

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Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 221))

Abstract

We describe some sufficient conditions for a J-dissipative operator in a Krein space to have maximal semidefinite invariant subspaces.T he 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.T he main conditions are given in the terms of the interpolation theory of Banach spaces.

Mathematics Subject Classification (2000). Primary 47B50; Secondary 46C20; 47D06.

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Authors and Affiliations

  1. Yugra State University, Chekhov st. 16, 628012, Hanty-Mansiisk, Russia

    S. G. Pyatkov

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  1. S. G. Pyatkov
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Correspondence to S. G. Pyatkov .

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Editors and Affiliations

  1. , Abt. Mathematik V, Universität Ulm, Ulm, 89069, Germany

    Wolfgang Arendt

  2. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  3. Institut für Mathematik, AG Modellierung, Numerik und, TU Berlin, Straße des 17 Juni 136, Berlin, 10623, Berlin, Germany

    Jussi Behrndt

  4. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Karl-Heinz Förster

  5. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Volker Mehrmann

  6. , Institut für Mathematik, TU Ilmenau, Weimarer Str. 25, Ilmenau, 98693, Thüringen, Germany

    Carsten Trunk

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Pyatkov, S.G. (2012). Maximal Semidefinite Invariant Subspaces for J-dissipative Operators. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_33

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