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Journal of Operator Theory

Volume 50, Issue 1, Summer 2003  pp. 107-117.

Countably hypercyclic operators

Authors Nathan S. Feldman
Author institution: Washington and Lee University, Lexington, VA 24450, USA

Summary:  Motivated by Herrero's conjecture on finitely hypercyclic operators, we define countably hypercyclic operators and establish a Countably Hypercyclic Criterion that is surprisingly similar to the well known Hypercyclicity Criterion. Our results support the idea that there is a countable version of Herrero's Conjecture for invertible operators. We use our criterion to characterize the hyponormal operators whose adjoints are countably hypercyclic and to give examples of countably hypercyclic operators that are not cyclic.

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