SUPERCYCLIC AND CESÀRO HYPERCYCLIC WEIGHTED TRANSLATIONS ON GROUPS

Abstract

Let $G$ be a locally compact group and let $1 \leq p \lt \infty$. We characterize supercyclic weighted translation operators on the Lebesgue space $L^p(G)$ in terms of the weight. Using this result, the characterization for Cesàro hypercyclic weighted translation operators is given. We also determine when scalar multiples of weighted translation operators are hypercyclic and topologically mixing, and show, for any weighted translation operator $T$, $\beta T$ is mixing for all $\beta \in (1,4)$ if $T$ and $4T$ are mixing.