On Joint Functional Calculus For Ritt Operators

TL;DR

This paper explores the joint functional calculus for multiple Ritt operators, providing characterizations of boundedness, and extending results to non-commutative $L^p$-spaces, with new transfer principles and dilation techniques.

Contribution

It introduces a new characterization of bounded joint functional calculus for Ritt operators on $L^p$-spaces and extends the theory to non-commutative settings with transfer principles and dilation results.

Findings

Characterization of boundedness for joint functional calculus.

Extension of results to non-commutative $L^p$-spaces.

Development of a multivariable transfer principle.

Abstract

In this paper, we study joint functional calculus for commuting $n$-tuple of Ritt operators. We provide an equivalent characterisation of boundedness for joint functional calculus for Ritt operators on $L^p$-spaces, $1< p<\infty$. We also investigate joint similarity problem and joint bounded functional calculus on non-commutative $L^p$-spaces for $n$-tuple of Ritt operators. We get our results by proving a suitable multivariable transfer principle between sectorial and Ritt operators as well as an appropriate joint dilation result in a general setting.