Common hypercyclic vectors for families of operators

Gallardo-Gutierrez, Eva; Partington, Jonathan

doi:10.1090/S0002-9939-07-09053-3

Common hypercyclic vectors for families of operators
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by Eva A. Gallardo-Gutierrez and Jonathan R. Partington

Proc. Amer. Math. Soc. 136 (2008), 119-126

DOI: https://doi.org/10.1090/S0002-9939-07-09053-3

Published electronically: September 25, 2007

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Abstract:

We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by Abakumov and Gordon and also Bayart. The criterion is applied to other specific families of operators.

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