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

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 ${\mathcal{M}}_z$ 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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Cited by in corpus (2)

• Generalized multipliers for left-invertible operators and applications
• On Cauchy dual operator and duality for Banach spaces of analytic functions