On Joint Functional Calculus For Ritt Operators

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.

15 pages. This version is much shorter than the previous version and only significant results are included. Some of the theorems and lemmas in the previous version work only if we strengthen the hypothesis but this is a very minor change

References in corpus (1)

• Maximal theorems and square functions for analytic operators on Lp-spaces