HYPERCYCLICITY ON INVARIANT SUBSPACES Petersson, Henrik;
A continuous linear operator is called hypercyclic if there exists an such that the orbit is dense. We consider the problem: given an operator , hypercyclic or not, is the restriction to some closed invariant subspace hypercyclic? In particular, it is well-known that any non-constant partial differential operator p(D) on (entire functions) is hypercyclic. Now, if q(D) is another such operator, p(D) maps ker q(D) invariantly (by commutativity), and we obtain a necessary and sufficient condition on p and q in order that the restriction p(D) : ker q(D) ker q(D) is hypercyclic. We also study hypercyclicity for other types of operators on subspaces of .