Common upper frequent hypercyclicity
Volume 250 / 2020
Studia Mathematica 250 (2020), 1-18
MSC: Primary 47A16.
DOI: 10.4064/sm180410-10-9
Published online: 5 July 2019
Abstract
Considering a family of upper frequently hypercyclic operators we study the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for an uncountable family of operators to admit such vectors called common upper frequently hypercyclic vectors. Using this result, we then give a construction of such vectors. Finally, we derive some applications to families of weighted shifts.
