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Article Dans Une Revue Bulletin of the Australian Mathematical Society Année : 2019

NEW COUNTEREXAMPLES ON RITT OPERATORS, SECTORIAL OPERATORS AND -BOUNDEDNESS

Résumé

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.
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Dates et versions

hal-03525915 , version 1 (14-01-2022)

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Citer

Loris Arnold, Christian Le Merdy. NEW COUNTEREXAMPLES ON RITT OPERATORS, SECTORIAL OPERATORS AND -BOUNDEDNESS. Bulletin of the Australian Mathematical Society, 2019, 100 (3), pp.498-506. ⟨10.1017/S0004972719000431⟩. ⟨hal-03525915⟩
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