Supercyclicity in the operator algebra

Alfonso Montes-Rodríguez, and M. Carmen Romero-Moreno. "Supercyclicity in the operator algebra." Studia Mathematica 150.3 (2002): 201-213. <http://eudml.org/doc/285115>.

@article{AlfonsoMontes2002,
abstract = {We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that certain supercyclic operators defined on a Banach space have an infinite-dimensional closed subspace of supercyclic vectors.},
author = {Alfonso Montes-Rodríguez, M. Carmen Romero-Moreno},
journal = {Studia Mathematica},
keywords = {operator algebra; separable Banach space; strong operator topology; supercyclic vector; hypercyclic vector; hypercyclicity of operators; supercyclicity; multiplication operators},
language = {eng},
number = {3},
pages = {201-213},
title = {Supercyclicity in the operator algebra},
url = {http://eudml.org/doc/285115},
volume = {150},
year = {2002},
}

TY - JOUR
AU - Alfonso Montes-Rodríguez
AU - M. Carmen Romero-Moreno
TI - Supercyclicity in the operator algebra
JO - Studia Mathematica
PY - 2002
VL - 150
IS - 3
SP - 201
EP - 213
AB - We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that certain supercyclic operators defined on a Banach space have an infinite-dimensional closed subspace of supercyclic vectors.
LA - eng
KW - operator algebra; separable Banach space; strong operator topology; supercyclic vector; hypercyclic vector; hypercyclicity of operators; supercyclicity; multiplication operators
UR - http://eudml.org/doc/285115
ER -