The Laplacian of an operator and the radial Toeplitz algebra

TL;DR

This paper explores the properties of the Laplacian operator within the radial Toeplitz algebra on Fock space, utilizing quantum harmonic analysis to simplify Gelfand theory applications.

Contribution

It demonstrates the density of the Laplacian's domain in the Toeplitz algebra and offers a streamlined approach to Gelfand theory for the radial Toeplitz algebra.

Findings

Laplacian domain is dense in the Toeplitz algebra

Simplified Gelfand theory for the radial Toeplitz algebra

Application of quantum harmonic analysis techniques

Abstract

Using tools from quantum harmonic analysis, we show that the domain of the Laplacian of an operator is dense in the Toeplitz algebra over the Fock space $\mathcal{F}^2(\mathbb{C}^n)$. As an application, we provide a simplified treatment of the Gelfand theory of the radial Toeplitz algebra.