Invariant subspaces for products of Hermitian operators
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- by Heydar Radjavi and Peter Rosenthal PDF
- Proc. Amer. Math. Soc. 43 (1974), 483-484 Request permission
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
- 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 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.
- Noboru Suzuki, Reduction theory of operators on Hilbert space–the invariant subspace problem, Indiana Univ. Math. J. 20 (1971), no. 10, 953–958. MR 405131, DOI 10.1512/iumj.1971.20.20089
Additional Information
- © Copyright 1974 American Mathematical Society
- 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