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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.

Keywords: $C_{0}(N)$-operator, reducing subspaces, model space, truncated Toeplitz operator

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