Dense range perturbations of hypercyclic operators

Luis Bernal-Gonzalez. "Dense range perturbations of hypercyclic operators." Colloquium Mathematicae 91.2 (2002): 283-292. <http://eudml.org/doc/283570>.

@article{LuisBernal2002,
abstract = {We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators and sequences which are hypercyclic in a weaker sense are shown. Our results extend and improve a result on denseness due to C. Kitai.},
author = {Luis Bernal-Gonzalez},
journal = {Colloquium Mathematicae},
keywords = {almost hypercyclic operators and sequences; totally weakly non-dense; totally weakly nowhere dense; perturbation; generalized kernel; one-to-one sequence; dense range sequence},
language = {eng},
number = {2},
pages = {283-292},
title = {Dense range perturbations of hypercyclic operators},
url = {http://eudml.org/doc/283570},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Luis Bernal-Gonzalez
TI - Dense range perturbations of hypercyclic operators
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 2
SP - 283
EP - 292
AB - We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators and sequences which are hypercyclic in a weaker sense are shown. Our results extend and improve a result on denseness due to C. Kitai.
LA - eng
KW - almost hypercyclic operators and sequences; totally weakly non-dense; totally weakly nowhere dense; perturbation; generalized kernel; one-to-one sequence; dense range sequence
UR - http://eudml.org/doc/283570
ER -