Generalized Volterra companion operators on Fock spaces

TL;DR

This paper characterizes the boundedness and compactness of generalized Volterra companion operators on Fock spaces, providing new insights into their properties and asymptotic behavior.

Contribution

It offers a complete characterization of these operators and proves the nonexistence of nontrivial compact Volterra companion operators on Fock spaces.

Findings

No nontrivial compact Volterra companion operators exist on Fock spaces.

Provides asymptotic estimates for the operator norms.

Characterizes bounded and compact operators between Fock spaces.

Abstract

We characterize the bounded and compact generalized Volterra companion integral operators on Fock spaces acting between the standard Fock spaces. As a special case, we prove that there exist no nontrivial compact Volterra companion integral and multiplication operators on Fock spaces. We also obtain asymptotic estimates for the norm of these operators.