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Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces

  • Christian Mehl
  • André C.M. Ran
  • Leiba Rodman
Part of the Operator Theory: Advances and Applications book series (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.

Keywords

Krein spaces polar decompositions normal operators indefinite inner products 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Christian Mehl
    • 1
  • André C.M. Ran
    • 2
  • Leiba Rodman
    • 3
  1. 1.Institut für Mathematik, MA 4-5Technische Universität BerlinBerlinGermany
  2. 2.Afdeling Wiskunde Faculteit der Exacte WetenschappenVrije Universiteit AmsterdamAmsterdamThe Netherlands
  3. 3.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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