Limits of hypercyclic operators on Hilbert spaces

Abstract

This article concerns the operators T E L(H), defined on a separable Hilbert space H, that belong to the norm closure HC(H) in L(H) of the set HC(H) of all hypercyclic operators. Starting from a Herrero's characterization of these operators [11] we deduce some criteria that are very useful in many concrete cases. We also show that if T E L(H) is invertible then T E HC(H) if and only if T-1 E HC(H). This result extends to HC(H) a known result of Kitai and Herrero established for hypercyclic operators, ([13]). (c) 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).