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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyperinvariant subspaces of $C_{11}$ contractions
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by Pei Yuan Wu PDF
Proc. Amer. Math. Soc. 75 (1979), 53-58 Request permission

Abstract:

For an operator T on a Hilbert space let Hyperlat T denote its hyperinvariant subspace lattice. Assume that T is a completely nonunitary ${C_{11}}$ contraction with finite defect indices. In this note we characterize the elements of Hyperlat T among invariant subspaces for T in terms of their corresponding regular factorizations and show that elements in Hyperlat T are exactly the spectral subspaces of T defined by Sz.-Nagy and Foiaş. As a corollary, if ${T_1},{T_2}$ are two such operators which are quasi-similar to each other, then Hyperlat ${T_1}$ is (lattice) isomorphic to Hyperlat ${T_2}$.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 75 (1979), 53-58
  • MSC: Primary 47A45; Secondary 47A15
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0529212-2
  • MathSciNet review: 529212