Topological structure of the space of (weighted) composition operators between Fock spaces in several variables

TL;DR

This paper characterizes the topological structure of spaces of (weighted) composition operators between Fock spaces in several variables, identifying connected components and isolated points.

Contribution

It provides explicit descriptions of all path connected components and isolated points in spaces of composition and weighted composition operators between Fock spaces.

Findings

Identifies all path connected components of the operator spaces

Characterizes isolated points within these spaces

Provides explicit descriptions of the topological structure

Abstract

We give explicit descriptions of all path connected components and isolated points of both spaces of composition operators and nonzero weighted composition operators acting from a Fock space $\mathcal{F}^p(\mathbb{C}^n)$ to another one $\mathcal{F}^q(\mathbb{C}^n)$.