Hyperinvariant subspaces of 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 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 are two such operators which are quasi-similar to each other, then Hyperlat is (lattice) isomorphic to Hyperlat .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0529212-2

Keywords:
Hyperinvariant subspace,
contraction,
quasi-similarity,
Jordan model for contractions

Article copyright:
© Copyright 1979
American Mathematical Society