In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...

We obtain a Disjoint Frequent Hypercyclicity Criterion and show that it characterizes disjoint frequent hypercyclicity for family of unilateral pseudo-shifts on c0(N) ?p(N), 1?p<?. As an application, we characterize frequently hypercyclic weighted shifts. give analogous results the weaker notions upper reiterative hypercyclicity. Finally, provide counterexamples showing that, although hypercycl...

We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω . The orbit is taken with respect to any fixed nonscalar differential operator generated by an entire function of subexponential type, thereby ext...