21787 articles – 15600 references  [version française]
 HAL: hal-00697603, version 2
 arXiv: 1205.3575
 Available versions: v1 (2012-05-15) v2 (2012-05-16)
 $n$-supercyclic and strongly $n$-supercyclic operators in finite dimension
 (2012-05-10)
 We prove that on $\mathbb{R}^n$, there is no $N$-supercyclic operator with $1\leq N< \lfloor \frac{n+1}{2}\rfloor$ i.e. if $\mathbb{R}^n$ has an $N$ dimensional subspace whose orbit under $T$ is dense in $\mathbb{R}^n$, then $N$ is greater than $\lfloor\frac{n+1}{2}\rfloor$. Moreover, this value is optimal. We then consider the case of strongly $N$-supercyclic operators. An operator $T$ is strongly $N$-supercyclic if $\mathbb{R}^n$ has an $N$-dimensional subspace whose orbit under $T$ is dense in $\mathbb{P}_N(\mathbb{R}^n)$, the $N$-th Grassmannian. We prove that strong $N$-supercyclicity does not occur non-trivially in finite dimension.
 1: Laboratoire de Mathématiques CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II
 Subject : Mathematics/Functional Analysis
 Keyword(s): n-supercyclicity – n-supercyclic operators – strong n-supercyclicity – strongly n-supercyclic operators – Jordan decomposition – finite dimension – supercyclic operators
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 hal-00697603, version 2 http://hal.archives-ouvertes.fr/hal-00697603 oai:hal.archives-ouvertes.fr:hal-00697603 From: Romuald Ernst <> Submitted on: Tuesday, 15 May 2012 17:45:37 Updated on: Wednesday, 16 May 2012 08:54:30