On functional calculus properties of Ritt operators
Florence Lancien, Christian Le Merdy
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Source: Crossref
Published: Nov 26, 2015
DOI: 10.1017/s0308210515000281
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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.
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