$n$-supercyclic and strongly $n$-supercyclic operators in finite dimensions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Studia Mathematica Année : 2014

$n$-supercyclic and strongly $n$-supercyclic operators in finite dimensions

Romuald Ernst

Résumé

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.
Fichier principal
Vignette du fichier
nsupercyclicityandstongnsupercyclicityinfinitedimensionpublic.pdf (590.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00697603 , version 1 (15-05-2012)
hal-00697603 , version 2 (15-05-2012)
hal-00697603 , version 3 (25-07-2013)
hal-00697603 , version 4 (06-01-2014)

Identifiants

Citer

Romuald Ernst. $n$-supercyclic and strongly $n$-supercyclic operators in finite dimensions. Studia Mathematica, 2014, 220, pp.15-53. ⟨10.4064/sm220-1-2⟩. ⟨hal-00697603v4⟩
149 Consultations
200 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More