The Herrero conditions on norm limits of hypercyclic operators

Abstract

Abstract. For a separable infinite dimensional Banach space X it is known that X supports many bounded linear operators T which are hypercyclic, that is such that there is a vector x E X with dense orbit {x, Tx, T2x,...}. Here we investigate the operator norm closure of the class of hypercyclic operator on X and of various subclasses that have been considered extensively in recent literature. In the case of a Hilbert space the norm closures we consider are all known to be characterised by conditions of Herrero.