Toeplitz Operators in a Symmetrically-Normed Ideal

TL;DR

This paper characterizes when fractional powers of Toeplitz operators with positive measure symbols belong to symmetrically normed ideals on the Fock space, advancing understanding of operator ideal membership in functional analysis.

Contribution

It provides a new characterization for fractional powers of Toeplitz operators with positive symbols in terms of symmetrically normed ideals, extending previous operator theory results.

Findings

Fractional powers of Toeplitz operators are characterized within symmetrically normed ideals.

The results apply to Toeplitz operators on the Fock (Segal-Bargmann) space.

The paper establishes criteria for operator ideal membership based on the measure symbol.

Abstract

We look at Toeplitz operators $T_\nu$ on the Fock Space (also known as the Segal-Bargmann space) which have a positive Borel measure $\nu$ as a symbol. We characterize when $\left(T_\nu\right)^s$ for $0<s\leq 1$ is in the symmetrically normed ideal associated with any given symmetric norming function.