A hypercyclicity criterion with applications

A continuous linear operator T :X →X on a topological vector space X is called hypercyclic if there is x ∈ X such that the orbit {T nx}n 0 is dense in X. We establish a criterion for hypercyclicity, and study some applications. In particular, we establish hypercyclic left-multipliers LT : S →T S 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. © 2006 Elsevier Inc. All rights reserved