On functional calculus properties of Ritt operators
Functional Analysis
2013-01-22 v1 Operator Algebras
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 (that is, T is polynomially bounded) but T does not have any bounded \H^\infty functional calculus with respect to a Stolz domain of 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.
Cite
@article{arxiv.1301.4875,
title = {On functional calculus properties of Ritt operators},
author = {Florence Lancien and Christian Le Merdy},
journal= {arXiv preprint arXiv:1301.4875},
year = {2013}
}