A hypercyclicity criterion with applications

A continuous linear operator on a topological vector space X is called hypercyclic if there is x∈X such that the orbit {Tnx}n⩾0 is dense in X. We establish a criterion for hypercyclicity, and study some applications. In particular, we establish hypercyclic left-multipliers on the space L(X,Y) of continuous linear operators between X and Y, provided with the topology of uniform convergence on bounded sets, for some spaces X,Y of holomorphic functions.