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arXiv · 1808.03339

A Shimorin-type analytic model on an annulus for left-invertible operators and applications

Pawel Pietrzycki
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Abstract

A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a left-invertible operator $T$, which satisfies certain conditions can be modelled as a multiplication operator $\mathscr{M}_z$ on a reproducing kernel Hilbert space of vector-valued analytic functions on an annulus or a disc. A similar result for composition operators in $\ell^2$-spaces is established.

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Pawel Pietrzycki. 2025-04-27. A Shimorin-type analytic model on an annulus for left-invertible operators and applications. https://doi.org/10.1016/j.jmaa.2019.04.027

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