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arXiv · 2307.06923

Invariant subspaces of the Cesaro operator

Eva A. Gallardo-Gutierrez·Jonathan R. Partington·William T. Ross
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Abstract

This paper explores various classes of invariant subspaces of the classical Cesàro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of the first two authors, and determine exactly which model spaces are $C$-invariant subspaces. We also describe the $C$-invariant subspaces contained in model spaces and establish that they are all cyclic. Along the way, we re-examine an associated Hilbert space of analytic functions on the unit disk developed by Kriete and Trutt. We also make a connection between the adjoint of the Cesàro operator and certain composition operators on $H^2$ which have universal translates in the sense of Rota.

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Eva A. Gallardo-Gutierrez, Jonathan R. Partington, William T. Ross. 2023-11-27. Invariant subspaces of the Cesaro operator. https://arxiv.org/abs/2307.06923

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