Co-Toeplitz Quantization: A Simple Case

TL;DR

This paper introduces a simplified specific case of co-Toeplitz quantization, a dual operator class to Toeplitz operators, with examples illustrating its properties and potential applications in categorical duality.

Contribution

It presents a new, simpler particular case of co-Toeplitz quantization, expanding the understanding of dual operator classes in quantization schemes.

Findings

Introduces a simple particular case of co-Toeplitz quantization

Provides examples demonstrating properties of the new quantization method

Highlights the categorical duality to Toeplitz operators

Abstract

The author has introduced in a recent paper a new class of operators, called co-Toeplitz operators, with symbols in a co-algebra. This is the categorical dual to Toeplitz operators which have symbols in an algebra. The mapping from a symbol to its co-Toeplitz operator gives a quantization scheme, called co-Toeplitz quantization. A new, quite simple particular case of co-Toeplitz quantization is introduced in this note. Examples are given in order to show some of its properties.