Common hypercyclic vectors for families of backward shift operators

Abstract

We provide necessary and sufficient conditions on the existence of com- mon hypercyclic vectors for multiples of the backward shift operator along sparse pow- ers. Our main result strongly generalizes corresponding results which concern the full orbit of the backward shift. Some of our results are valid in a more general context, in the sense that they apply for a wide class of hypercyclic operators. MSC (2010): 47A16