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Invariant Subspaces of Infinite Dimensional Hamiltonians and Solutions of the Corresponding Riccati Equations

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Linear Operators and Matrices

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 130))

Abstract

We consider an infinite dimensional algebraic Riccati equation which arises in systems theory. Using a dichotomy property of the corresponding Hamiltonian and results on invariant subspaces of operators in spaces with an indefinite inner product we show the existence of bounded and unbounded solutions of this Riccati equation.

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Author information

Authors and Affiliations

  1. Institut für Analysis und Technische Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, Wien, A-1040, Austria

    H. Langer

  2. Faculteit Exacte Wetenschappen Divisie Wiskunde en Informatica, Vrije Universiteit Amsterdam, De Boelelaan 1081a, Amsterdam, 1081 HV, The Netherlands

    A. C. M. Ran

  3. Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, Leiden, 2333 CA, The Netherlands

    B. A. van de Rotten

Authors
  1. H. Langer
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  2. A. C. M. Ran
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  3. B. A. van de Rotten
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler, Faculty of Exact Sciences Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8–10/1411, Wien, 1040, Austria

    H. Langer

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© 2002 Springer Basel AG

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Langer, H., Ran, A.C.M., van de Rotten, B.A. (2002). Invariant Subspaces of Infinite Dimensional Hamiltonians and Solutions of the Corresponding Riccati Equations. In: Gohberg, I., Langer, H. (eds) Linear Operators and Matrices. Operator Theory: Advances and Applications, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8181-4_18

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  • DOI: https://doi.org/10.1007/978-3-0348-8181-4_18

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9467-8

  • Online ISBN: 978-3-0348-8181-4

  • eBook Packages: Springer Book Archive

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