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arXiv · 2505.05788

$H^\infty$ Functional Calculus for a Commuting Pair of $\text{Ritt}_{\text{E}}$ Operators

Suman Mondal·Subhajit Palai·Samya Kumar Ray
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Abstract

In this article, we develop a framework for the joint functional calculus of commuting pair of $\text{Ritt}_{\text{E}}$ operators on Banach spaces. We establish a transfer principle that relates the bounded holomorphic functional calculus for pair of $\text{Ritt}_{\text{E}}$ operators to that of their associated sectorial counterparts. In addition, we prove a joint dilation theorem for commuting tuples of $\text{Ritt}_{\text{E}}$ operators on a broad class of Banach spaces. As a key application, we obtain an equivalent set of criteria on $L^p$-spaces for $1<p< \infty$ that determine when a commuting pair of $\text{Ritt}_{\text{E}}$ operators admits a joint bounded functional calculus.

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Suman Mondal, Subhajit Palai, Samya Kumar Ray. 2025-05-09. $H^\infty$ Functional Calculus for a Commuting Pair of $\text{Ritt}_{\text{E}}$ Operators. https://arxiv.org/abs/2505.05788

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