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Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems pp 277–292Cite as

Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 162))

Abstract

Polar decompositions of normal matrices in indefinite inner product spaces are studied. The main result of this paper provides sufficient conditions for a normal operator in a Krein space to admit a polar decomposition. As an application of this result, we show that any normal matrix in a finite-dimensional indefinite inner product space admits a polar decomposition which answers affirmatively an open question formulated in [2]. Furthermore, necessary and sufficient conditions are given for a matrix to admit a polar decomposition and for a normal matrix to admit a polar decomposition with commuting factors.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, MA 4-5, Technische Universität Berlin, D-10623, Berlin, Germany

    Christian Mehl

  2. Afdeling Wiskunde Faculteit der Exacte Wetenschappen, Vrije Universiteit Amsterdam, De Boelelaan 1081a, NL-1081 HV, Amsterdam, The Netherlands

    André C.M. Ran

  3. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Leiba Rodman

Authors
  1. Christian Mehl
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  2. André C.M. Ran
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  3. Leiba Rodman
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, D-10623, Berlin, Germany

    Karl-Heinz Förster  & Peter Jonas  & 

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, A-1040, Wien, Austria

    Heinz Langer

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Mehl, C., Ran, A.C., Rodman, L. (2005). Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces. In: Förster, KH., Jonas, P., Langer, H. (eds) Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems. Operator Theory: Advances and Applications, vol 162. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7453-5_15

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