Acta Applicandae Mathematica

, Volume 27, Issue 1–2, pp 1–22 | Cite as

Positive operators on Krein spaces

  • Y. A. Abramovich
  • C. D. Aliprantis
  • O. Burkinshaw


A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.

Mathematics Subject Classifications (1991)

46C50 47B65 47B37 

Key words

partially ordered Banach space Krein space Krein operator hyperinvariant subspace 


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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Y. A. Abramovich
    • 1
  • C. D. Aliprantis
    • 1
  • O. Burkinshaw
    • 1
  1. 1.Department of MathematicsIUPUIIndianapolisU.S.A

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