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 $\mathcal{F}(\mathbb{C}^d)$ 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 $\mathcal{F}(\mathbb{C}^d)$.

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

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