Cyclicity of composition operators on the Fock space

TL;DR

This paper fully characterizes cyclic composition operators on the d-dimensional Fock space, explores their supercyclicity and convex-cyclicity, and computes approximation numbers of compact operators, advancing understanding of their spectral properties.

Contribution

Provides a complete characterization of cyclic composition operators on the Fock space and analyzes their supercyclicity, convex-cyclicity, and approximation numbers.

Findings

Characterization of cyclic composition operators in terms of their symbol

Analysis of supercyclicity and convex-cyclicity properties

Calculation of approximation numbers for compact composition operators

Abstract

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