Limits of hypercyclic operators on Hilbert spaces

This article concerns the operators T ∈ L ( H ) , defined on a separable Hilbert space H , that belong to the norm closure H C ( H ) ‾ in L ( H ) of the set H C ( 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 ∈ L ( H ) is invertible then T ∈ H C ( H ) ‾ if and only if T − 1 ∈ H C ( H ) ‾ . This result extends to H C ( H ) ‾ a known result of Kitai and Herrero established for hypercyclic operators, ( [13] ).