Hypercyclic sequences of PDE-preserving operators

A sequence of continuous linear operators is said to be hypercyclic if there exists a vector , called hypercyclic for , such that {T_nx:n0} is dense. A continuous linear operator, acting on some suitable function space, is PDE-preserving for a given set of convolution operators, when it map every kernel set for these operators invariantly. We establish hypercyclic sequences of PDE-preserving operators on , and study closed infinite-dimensional subspaces of, except for zero, hypercyclic vectors for these sequences.