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 ${T_2}$.References
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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