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The unicellularity of contractions of class $ C\sb 0$


Author: Cheng Zu Zou
Journal: Proc. Amer. Math. Soc. 119 (1993), 775-782
MSC: Primary 47A15; Secondary 47A45, 47A65
DOI: https://doi.org/10.1090/S0002-9939-1993-1163329-4
MathSciNet review: 1163329
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Abstract: In this paper, we shall generalize the unicellularity of operators on finite-dimensional spaces to that of the contraction of class $ {C_0}$ on Hilbert spaces.

We prove:

(1) Each nilpotent operator on Hilbert space is Banach reducible (Theorem 3).

(2) A contraction $ T$ of class $ {C_0}$ on Hilbert space is unicellular if and only if $ T$ has one-point spectrum and every invariant subspace for $ T$ is cyclic (Theorem 6).

(3) A contraction $ T$ of class $ {C_0}$ on Hilbert space is unicellular if and only if $ T$ has one-point spectrum and all invariant subspaces of $ T$ are hyperinvariant subspaces of $ T$ (Theorem 8).


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1163329-4
Article copyright: © Copyright 1993 American Mathematical Society

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