Two remarks on frequent hypercyclicity

[摘要] We show that if T : X -> X is a continuous linear operator on an F-space X not equal {0}, then the set of frequently hypercyclic vectors of T is of first category. in X, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T : X -> X is a bounded linear operator on a Banach space X not equal {0} and if T is frequently hypercyclic (or, more generally, syndetically transitive), then the T*-orbit of every non-zero element of X* is bounded away from 0, and in particular T* is not hypercyclic. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Frequently hypercyclic operator;Baire category;Syndetically transitive operator