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Journal of Operator Theory

Volume 92, Issue 2,  Autumn  2024  pp. 549-577.

Cyclicity of composition operators on the Fock spaceCyclicity of composition operators on the Fock space

Authors:  Frederic Bayart (1) and Sebastian Tapia-Garcia (2)
Author institution: (1) Laboratoire de Mathematiques Blaise Pascal UMR 6620 CNRS, Universite Clermont Auvergne, Campus universitaire Cezeaux, 3 place Vasarely, 63178 Aubiere Cedex, France
(2) Laboratoire de Mathematiques Blaise Pascal UMR 6620 CNRS, Universite Clermont Auvergne, Campus universitaire Cezeaux, 3 place Vasarely, 63178 Aubiere Cedex, France


Summary:  In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space F(Cd) in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type of operators. We end this work by computing the approximation numbers of compact composition operators defined on F(Cd).

DOI: http://dx.doi.org/10.7900/jot.2022nov10.2419
Keywords:  composition operators, Fock space, cyclic operators

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