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

• Autorzy: Romuald Ernst
• Języki publikacji: EN

Abstrakty

EN

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 $T ∈ 𝓛(ℝ^{N})$ 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 $T ∈ 𝓛(ℝ^{N})$ is strongly n-supercyclic if $ℝ^{N}$ has an n-dimensional subspace whose orbit under T is dense in $ℙₙ(ℝ^{N})$, the nth Grassmannian. We prove that strong n-supercyclicity does not occur non-trivially in finite dimensions.

Kategorie tematyczne

• 15A21: Canonical forms, reductions, classification
• 47A16: Cyclic vectors, hypercyclic and chaotic operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 220
• Numer: 1
• Strony: 15-53

Daty

wydano

2014

Twórcy

autor

Romuald Ernst

• Clermont Université, UniversitéBlaise Pascal, Laboratoire de Mathématiques, bp 10448, F-63000 Clermont-Ferrand, France
• CNRS, UMR 6620, Laboratoire de Mathématiques, F-63177 Aubière, France

Identyfikatory

DOI

10.4064/sm220-1-2