$\Gamma$-supercyclicity for Bilateral Shift Operators and Translation Semigroups

Abstract

We characterize the $\Gamma$-supercyclicity of bilateral shift operators and translation semigroups in weighted $L^p$ spaces in terms of the weight and $\Gamma$. We survey the notion of $S$-density introduced by E. Abakumov and Y. Kuznetsova. Finally, we present without proof some characterization of a supercyclic version for the $S$-density of translation operator.