A hypercyclicity criterion for non-metrizable topological vector spaces

Abstract

[EN] We provide a sufficient condition for an operator T on a non-metrizable and sequentially separable topological vector space X to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on ]0; 1[, which solves two problems of Bonet and Domanski [3], and the ¿snake shift¿ constructed in [5] on direct sums of sequence spaces. The two examples have in common that they do not admit a densely embedded F-space Y for which the operator restricted to Y is continuous and hypercyclic, i.e., the hypercyclicity of these operators cannot be a consequence of the comparison principle with hypercyclic operators on F-spaces.