Perturbation of hypercyclic and supercyclic operators

The first chapter talks about sets of cyclic, supercyclic, hypercyclic and superfull vectors. We will show that for a vector to be super- or hypercyclic excludes the possibility of its being superfull. Next we will apply the concept of sigma-porous sets to these types of sets in the specific case of the weighted backward shift. The second chapter talks about the perturbation of super- and hypercyclic operators and we will show that each super- or hypercyclic operator can be perturbed by an arbitrarily small one-dimensional operator, so that the resulting operator is no longer in the norm closure of the set of supercyclic operators. The last chapter gathers some facts about the perturbation of cyclic operators.