A local Szeg\"o-type theorem in Toeplitz quantization

TL;DR

This paper presents a local Szeg"o-type theorem for Toeplitz operators within the context of positive line bundles on compact symplectic manifolds, extending previous global results to a local setting.

Contribution

It introduces a local version of the Szeg"o-type theorem for Toeplitz operators on symplectic manifolds, expanding the scope of earlier global theorems.

Findings

Established a local Szeg"o-type theorem for Toeplitz operators

Extended global results to local settings on symplectic manifolds

Provided new insights into Toeplitz quantization in geometric analysis

Abstract

A Szeg\"o-type theorem for Toeplitz operators was proved by Boutet de Monvel and Guillemin for general Toeplitz structures. We give a local version of this result in the setting of positive line bundles on compact symplectic manifolds.