A higher rank version of Kitai’s theorem

We prove that each linear action of Zn + on an infinite-dimensional Banach space generated by compact operators cannot be hypercyclic. This result generalizes a theorem of Kitai for the case of Z+ actions. Contrary to the case of infinite dimension, a hypercyclic action of Z3 + on C is given. © 2008 Elsevier Inc. All rights reserved