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Operator Theory and Boundary Eigenvalue Problems pp 176–205Cite as

Selfadjoint Extensions of a Closed Linear Relation of Defect One in a Krein Space

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 80))

Abstract

In this paper we study the selfadjoint and the nonnegative selfadjoint extensions of a nonnegative closed linear relation (c.l.r.) A0 of defect one in a Krein space (H, [·, ·]). These extensions are described by their resolvents, that is, M. G. Krein’s formula for the resolvents of the extensions of a symmetric densely defined operator with defect (1,1) is generalized to the situation considered here. The main difficulties which arise with this generalization are the following.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Postfach 601553, D-14415, Potsdam, Germany

    Peter Jonas

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

    Heinz Langer

Authors
  1. Peter Jonas
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  2. Heinz Langer
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

  2. Institut für Analysis, technische Mathematik und Versicherungsmathematik, TU Wien, 1040, Wien, Austria

    H. Langer

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Jonas, P., Langer, H. (1995). Selfadjoint Extensions of a Closed Linear Relation of Defect One in a Krein Space. In: Gohberg, I., Langer, H. (eds) Operator Theory and Boundary Eigenvalue Problems. Operator Theory: Advances and Applications, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9106-6_12

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  • DOI: https://doi.org/10.1007/978-3-0348-9106-6_12

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9909-3

  • Online ISBN: 978-3-0348-9106-6

  • eBook Packages: Springer Book Archive

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