Disjoint Hypercyclicity and Weighted Translations on Discrete Groups
Printed: Dec 2017
Let $1\leq p\lt \infty$, and let $G$ be a discrete group. We give
a sufficient and necessary condition
for weighted translation operators on the Lebesgue space $\ell^p(G)$
to be densely disjoint hypercyclic.
The characterization for the dual of a weighted translation to
be densely disjoint hypercyclic is also obtained.
disjoint hypercyclicity, topological transitivity, weighted translation, $\ell^p$-space
47A16 - Cyclic vectors, hypercyclic and chaotic operators
47B38 - Operators on function spaces (general)
43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.