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arXiv · 1301.4875

On functional calculus properties of Ritt operators

Florence Lancien·Christian Le Merdy
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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.

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Florence Lancien, Christian Le Merdy. 2013-01-21. On functional calculus properties of Ritt operators. https://arxiv.org/abs/1301.4875

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