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Integral Equations and Operator Theory

, Volume 56, Issue 1, pp 83–91 | Cite as

Invariant Maximal Positive Subspaces and Polar Decompositions

  • Christian MehlEmail author
  • André C. M. Ran
  • Leiba Rodman
Original Paper

Abstract.

It is proved that invertible operators on a Krein space which have an invariant maximal uniformly positive subspace and map its orthogonal complement into a nonnegative subspace allow polar decompositions with additional spectral properties. As a corollary, several classes of Krein space operators are shown to allow polar decompositions. An example in a finite dimensional Krein space shows that there exist dissipative operators that do not allow polar decompositions.

Mathematics Subject Classification (2000).

Primary 47B44 46C20 

Keywords.

Krein space invariant subspace dissipative operator polar decomposition 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Christian Mehl
    • 1
    Email author
  • André C. M. Ran
    • 2
  • Leiba Rodman
    • 3
  1. 1.Fakultät II, Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Afdeling Wiskunde, Faculteit der Exacte WetenschappenVrije Universiteit AmsterdamHV AmsterdamThe Netherlands
  3. 3.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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