On functional calculus properties of Ritt operators

Abstract

We compare various functional calculus properties of Ritt operators. We show the existence of a Ritt operator T: X → X on some Banach space X with the following property: T has a bounded H∞-functional calculus with respect to the unit disc 𝔻(that is, T is polynomially bounded) but T does not have any bounded H∞-functional calculus with respect to a Stolz domain of 𝔻 with vertex at 1. Also we show that for an R-Ritt operator the unconditional Ritt condition of Kalton and Portal is equivalent to the existence of a bounded H∞-functional calculus with respect to such a Stolz domain.