Common hypercyclic vectors and universal functions
Abstract
Let X,Y be two separable Banach or Frechet spaces , and (Tn) , n=1,2,... be a sequence from linear and continuous operators from X to Y . We say that the sequence (Tn) , n=1,2,... is universal , if there exists some vector v in X such that the sequence Tn(v) , n=1,2,... is dense in Y . If X=Y we say that the sequence (Tn) is hypercyclic .More generally we consider an uncountable subset A from complex numbers and for every fixed a in A we consider a sequence (Ta,n) , n=1,2,... from linear and continuous operators from X to Y .The problem of common universal or hypercyclic vectors is whether the uncountable family of sequences of operators (Ta,n) , n=1,2,... share a common universal vector for all a in A .We examine , in this work ,some specific cases of this problem for translation , differential , and backward shift operators . We study also some approximating problems about universal Taylor series .
Keywords
Cite
@article{arxiv.1511.06145,
title = {Common hypercyclic vectors and universal functions},
author = {George Costakis and Nikos Tsirivas},
journal= {arXiv preprint arXiv:1511.06145},
year = {2015}
}