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

Romuald Ernst

Romuald Ernst

Studia Mathematica, Tome 223 (2014), p. 15-53 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that on $ℝ^{N}$ , there is no n-supercyclic operator with 1 ≤ n < ⌊(N + 1)/2⌋, i.e. if $ℝ^{N}$ has an n-dimensional subspace whose orbit under $T \in (ℝ^{N})$ is dense in $ℝ^{N}$ , then n is greater than ⌊(N + 1)/2⌋. Moreover, this value is optimal. We then consider the case of strongly n-supercyclic operators. An operator $T \in (ℝ^{N})$ is strongly n-supercyclic if $ℝ^{N}$ has an n-dimensional subspace whose orbit under T is dense in $ℙ ₙ (ℝ^{N})$ , the nth Grassmannian. We prove that strong n-supercyclicity does not occur non-trivially in finite dimensions.

Publié le : 2014-01-01

Zbl 1296.47007

EUDML-ID : urn:eudml:doc:285856

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     author = {Romuald Ernst},
     title = {n-supercyclic and strongly n-supercyclic operators in finite dimensions},
     journal = {Studia Mathematica},
     volume = {223},
     year = {2014},
     pages = {15-53},
     zbl = {1296.47007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-2}
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Romuald Ernst. n-supercyclic and strongly n-supercyclic operators in finite dimensions. Studia Mathematica, Tome 223 (2014) pp. 15-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-2/