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Proceedings of the American Mathematical Society

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

 

 

Hyperinvariant subspaces of $ C\sb{11}$ contractions


Author: Pei Yuan Wu
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1979-0529212-2
Keywords: Hyperinvariant subspace, $ {C_{11}}$ contraction, quasi-similarity, Jordan model for $ {C_{11}}$ contractions
Article copyright: © Copyright 1979 American Mathematical Society