@article{RomualdErnst2014,
abstract = {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 $T ∈ (ℝ^\{N\})$ 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 $T ∈ (ℝ^\{N\})$ 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.},
author = {Romuald Ernst},
journal = {Studia Mathematica},
keywords = {hypercyclic; supercyclic; -supercyclic; strongly -supercyclic; finite dimension},
language = {eng},
number = {1},
pages = {15-53},
title = {n-supercyclic and strongly n-supercyclic operators in finite dimensions},
url = {http://eudml.org/doc/285856},
volume = {220},
year = {2014},
}
TY - JOUR
AU - Romuald Ernst
TI - n-supercyclic and strongly n-supercyclic operators in finite dimensions
JO - Studia Mathematica
PY - 2014
VL - 220
IS - 1
SP - 15
EP - 53
AB - 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 $T ∈ (ℝ^{N})$ 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 $T ∈ (ℝ^{N})$ 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.
LA - eng
KW - hypercyclic; supercyclic; -supercyclic; strongly -supercyclic; finite dimension
UR - http://eudml.org/doc/285856
ER -
