Topological structures of generalized Volterra-type integral operators

TL;DR

This paper investigates the properties and topological structures of generalized Volterra-type integral operators on Fock spaces, providing new characterizations and criteria for compactness and Schatten class membership.

Contribution

It introduces simpler growth and integrability conditions for these operators and analyzes their difference topologies, including a characterization of compact differences.

Findings

Difference of two Volterra-type operators is compact iff both are compact.

New criteria for operator compactness and Schatten class membership.

Simplified conditions for operator properties on Fock spaces.

Abstract

We study the generalized Volterra-type integral and composition operators acting on the classical Fock spaces. We first characterize various properties of the operators in terms of growth and integrability conditions which are simpler to apply than those already known Berezin type characterizations. Then, we apply these conditions to study the compact and Schatten $\mathcal{S}_p$ class difference topological structures of the space of the operators. In particular, we proved that the difference of two Volterra-type integral operators is compact if and only if both are compact.