Journal of Operator Theory
Volume 84, Issue 2, Fall 2020 pp. 259-288.
The reducibility of the power of a $C_{0}(1)$-operator
Authors:
Caixing Gu
Author institution: Department of Mathematics, California Polytechnic State University at San Luis Obispo, CA 93407, U.S.A.
Summary: Inspired by the work of Douglas and Foias in 2006 on the structure of the
square of a $C_{0}(1)$-operator, we form a conjecture about a certain
reducibility of any power $N$ of a $C_{0}(1)$-operator. We then prove this
conjecture for $N=3$ by determining explicitly the relevant reducing subspaces.
DOI: http://dx.doi.org/10.7900/jot.2018may02.2274
Keywords: $C_{0}(N)$-operator, reducing subspaces, model space, truncated Toeplitz operator
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