Some properties of N-supercyclic operators

P. S. Bourdon, N. S. Feldman, and J. H. Shapiro. "Some properties of N-supercyclic operators." Studia Mathematica 165.2 (2004): 135-157. <http://eudml.org/doc/285175>.

@article{P2004,
abstract = {Let T be a continuous linear operator on a Hausdorff topological vector space 𝓧 over the field ℂ. We show that if T is N-supercyclic, i.e., if 𝓧 has an N-dimensional subspace whose orbit under T is dense in 𝓧, then T* has at most N eigenvalues (counting geometric multiplicity). We then show that N-supercyclicity cannot occur nontrivially in the finite-dimensional setting: the orbit of an N-dimensional subspace cannot be dense in an (N+1)-dimensional space. Finally, we show that a subnormal operator on an infinite-dimensional Hilbert space can never be N-supercyclic.},
author = {P. S. Bourdon, N. S. Feldman, J. H. Shapiro},
journal = {Studia Mathematica},
keywords = {-supercyclic operators; subnormal operators},
language = {eng},
number = {2},
pages = {135-157},
title = {Some properties of N-supercyclic operators},
url = {http://eudml.org/doc/285175},
volume = {165},
year = {2004},
}

TY - JOUR
AU - P. S. Bourdon
AU - N. S. Feldman
AU - J. H. Shapiro
TI - Some properties of N-supercyclic operators
JO - Studia Mathematica
PY - 2004
VL - 165
IS - 2
SP - 135
EP - 157
AB - Let T be a continuous linear operator on a Hausdorff topological vector space 𝓧 over the field ℂ. We show that if T is N-supercyclic, i.e., if 𝓧 has an N-dimensional subspace whose orbit under T is dense in 𝓧, then T* has at most N eigenvalues (counting geometric multiplicity). We then show that N-supercyclicity cannot occur nontrivially in the finite-dimensional setting: the orbit of an N-dimensional subspace cannot be dense in an (N+1)-dimensional space. Finally, we show that a subnormal operator on an infinite-dimensional Hilbert space can never be N-supercyclic.
LA - eng
KW - -supercyclic operators; subnormal operators
UR - http://eudml.org/doc/285175
ER -