Path connected components of the space of Volterra-type integral operators

TL;DR

This paper explores the topological structure of Volterra-type integral operators on Fock spaces, revealing that the connected components are precisely the compact operators and characterizing isolated points within this space.

Contribution

It provides a detailed topological analysis of Volterra-type integral operators on Fock spaces, identifying connected components and isolated points.

Findings

Connected and path connected components are exactly the compact operators.

No essentially isolated Volterra-type integral operators exist.

Characterization of isolated points in the operator space.

Abstract

We study the topological structure of the space of Volterra-type integral operators on Fock spaces endowed with the operator norm. We proved that the space has the same connected and path connected components which is the set of all compact operators acting on the Fock spaces. We also obtained a characterization of isolated points of the space of the operators and showed that there exists no essentially isolated Volterra-type integral operator.