The unicellularity of contractions of class $C_ 0$
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- by Cheng Zu Zou PDF
- Proc. Amer. Math. Soc. 119 (1993), 775-782 Request permission
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
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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