This is an announcement for the paper "On functional calculus properties of Ritt operators" by Florence Lancien and Christian Le Merdy.

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 $\H^\infty$ functional calculus with respect to the unit disc $\D$ (that is, T is polynomially bounded) but T does not have any bounded $\H^\infty$ 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-Portal is equivalent to the existence of a bounded $\H^\infty$ functional calculus with respect to such a Stolz domain.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 47A60

Submitted from: clemerdy@univ-fcomte.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.4875

or

http://arXiv.org/abs/1301.4875