The unicellularity of contractions of class
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 | References | Similar Articles | Additional Information
Abstract: In this paper, we shall generalize the unicellularity of operators on finite-dimensional spaces to that of the contraction of class on Hilbert spaces.
We prove:
(1) Each nilpotent operator on Hilbert space is Banach reducible (Theorem 3).
(2) A contraction of class
on Hilbert space is unicellular if and only if
has one-point spectrum and every invariant subspace for
is cyclic (Theorem 6).
(3) A contraction of class
on Hilbert space is unicellular if and only if
has one-point spectrum and all invariant subspaces of
are hyperinvariant subspaces of
(Theorem 8).
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1993-1163329-4
Article copyright:
© Copyright 1993
American Mathematical Society