TL;DR
This paper investigates the existence of vectors that are upper frequently hypercyclic for all operators in a family, providing conditions for their existence and applications to weighted shift operators.
Contribution
It introduces sufficient conditions for common upper frequently hypercyclic vectors across families of operators and constructs such vectors, with applications to weighted shifts.
Findings
Established conditions for the existence of common upper frequently hypercyclic vectors.
Provided a construction method for these vectors.
Applied results to specific families of weighted shift operators.
Abstract
Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to have these 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.
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