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
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