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NEW COUNTEREXAMPLES ON RITT OPERATORS, SECTORIAL OPERATORS AND
$R$-BOUNDEDNESS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 3 / December 2019
- Published online by Cambridge University Press:
- 11 April 2019, pp. 498-506
- Print publication:
- December 2019
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- Article
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Let
${\mathcal{D}}$ be a Schauder decomposition on some Banach space 
$X$. We prove that if 
${\mathcal{D}}$ is not 
$R$-Schauder, then there exists a Ritt operator 
$T\in B(X)$ which is a multiplier with respect to 
${\mathcal{D}}$ such that the set 
$\{T^{n}:n\geq 0\}$ is not 
$R$-bounded. Likewise, we prove that there exists a bounded sectorial operator 
$A$ of type 
$0$ on 
$X$ which is a multiplier with respect to 
${\mathcal{D}}$ such that the set 
$\{e^{-tA}:t\geq 0\}$ is not 
$R$-bounded.
On functional calculus properties of Ritt operators
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 6 / December 2015
- Published online by Cambridge University Press:
- 26 November 2015, pp. 1239-1250
- Print publication:
- December 2015
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- Article
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