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Invariant subspaces for products of Hermitian operators


Authors: Heydar Radjavi and Peter Rosenthal
Journal: Proc. Amer. Math. Soc. 43 (1974), 483-484
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0512667-2
MathSciNet review: 0512667
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Abstract: It is shown that a nonscalar operator which is the product of a Hermitian operator and a positive operator has a nontrivial hyperinvariant subspace; this is a slight generalization of a result of Suzuki's.


References [Enhancements On Off] (What's this?)

  • [1] P. A. Fillmore, Notes on operator theory, Van Nostrand Reinhold Math. Studies, no. 30, Van Nostrand-Reinhold, New York, 1970. MR 41 #2414. MR 0257765 (41:2414)
  • [2] B. Sz.-Nagy and C. Foiaş, Analyse harmonique des opérateurs de l'espace de Hilbert, Masson, Paris; Akad. Kiadó, Budapest, 1967; English rev. transl., North-Holland, Amsterdam; American Elsevier, New York; Akad. Kiadó, Budapest, 1970. MR 37 #778; 43 #947.
  • [3] N. Suzuki, Reduction theory of operators on Hilbert space, Indiana Univ. Math. J. 20 (1971), 953-958. MR 0405131 (53:8926)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0512667-2
Keywords: Operators on Hilbert space, hyperinvariant subspace, positive, Hermitian
Article copyright: © Copyright 1974 American Mathematical Society

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