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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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] Peter A. Fillmore, Notes on operator theory, Van Nostrand Reinhold Mathematical Studies, No. 30, Van Nostrand Reinhold Co., New York-London-Melbourne, 1970. MR 0257765
  • [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] Noboru Suzuki, Reduction theory of operators on Hilbert space–the invariant subspace problem, Proceedings of an International Symposium on Operator Theory (Indiana Univ., Bloomington, Ind., 1970), 1971, pp. 953–958. MR 0405131, https://doi.org/10.1512/iumj.1971.20.20089

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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