Subprincipal symbol for Toeplitz operators

TL;DR

This paper develops subprincipal symbol estimates for Berezin-Toeplitz operators on symplectic manifolds, introduces a family of subprincipal symbol maps, and proves their uniqueness under certain conditions.

Contribution

It provides the first construction and characterization of subprincipal symbol maps for Berezin-Toeplitz operators on symplectic manifolds.

Findings

Established subprincipal estimates for Berezin-Toeplitz operators.

Constructed a family of subprincipal symbol maps.

Proved the uniqueness of these maps under specific conditions.

Abstract

We establish some subprincipal estimates for Berezin-Toeplitz operators on symplectic compact manifolds. From this, we construct a family of subprincipal symbol maps and we prove that these maps are the only ones satisfying some expected conditions.