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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
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.

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  • [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,

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Keywords: Operators on Hilbert space, hyperinvariant subspace, positive, Hermitian
Article copyright: © Copyright 1974 American Mathematical Society

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