Hypercyclic bilinear operators on Banach spaces

Abstract

We study the dynamics induced by an m-linear operator. We answer a question of Bès and Conejero showing an example of an m-linear hypercyclic operator acting on a Banach space. Moreover, we prove the existence of m-linear hypercyclic operators on arbitrary infinite dimensional separable Banach spaces. We also prove an existence result about symmetric bihypercyclic bilinear operators, answering a question by Grosse-Erdmann and Kim.