Hypercyclic behaviour of operators in a hypercyclic C-0-semigroup

摘要

Let {T-t}(t) >= 0 be a hypercyclic strongly continuous semigroup of operators. Then each T-t (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C-0-semigroups. The analogous result for frequent hypercyclicity is also obtained. (c) 2006 Elsevier Inc. All rights reserved.