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Positive Operators on Krein Spaces

In: Positive Operators and Semigroups on Banach Lattices

Author

Listed:
  • Y. A. Abramovich

    (IUPUI, Department of Mathematics)

  • C. D. Aliprantis

    (IUPUI, Department of Mathematics)

  • O. Burkinshaw

    (IUPUI, Department of Mathematics)

Abstract

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.

Suggested Citation

  • Y. A. Abramovich & C. D. Aliprantis & O. Burkinshaw, 1992. "Positive Operators on Krein Spaces," Springer Books, in: C. B. Huijsmans & W. A. J. Luxemburg (ed.), Positive Operators and Semigroups on Banach Lattices, pages 1-22, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2721-1_1
    DOI: 10.1007/978-94-017-2721-1_1
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