Existence of Hypercyclic Operators on Topological Vector Spaces

The present paper introduces a very simple, but very useful notion of the so called quasi-extension ofl1-operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators. In particular, it answers in the affirmative a question of S. Rolewicz, posed in 1969,whether or not every infinite dimensional separable Banach space admits a continuous hypercyclic operator.