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Pré-Publication, Document De Travail Année : 2015

COMMON HYPERCYCLIC VECTORS FOR HIGH DIMENSIONAL FAMILIES OF OPERATORS

Résumé

Let $(T_\lambda)_{\lambda\in\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of $\mathbb R^d$. We give sufficient conditions on the family to yield the existence of a vector $x\in X$ such that, for any $\lambda\in\Lambda$, the set $\big\{T_\lambda^n x;\ n\geq 1\big\}$ is dense in $X$. We obtain results valid for any value of $d\geq 1$ whereas the previously known results where restricted to $d=1$. Our methods also shed new light on the one-dimensional case.
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Dates et versions

hal-01136343 , version 1 (27-03-2015)

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Frédéric Bayart. COMMON HYPERCYCLIC VECTORS FOR HIGH DIMENSIONAL FAMILIES OF OPERATORS. 2015. ⟨hal-01136343⟩
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