Spectral theorem approach to commutative C* -algebras generated by Toeplitz operators on the unit ball: quasi-elliptic related cases

TL;DR

This paper introduces a spectral theorem-based approach to analyze commutative C*-algebras generated by Toeplitz operators on the unit ball, providing a new representation for elliptic type algebras as functions of commuting unbounded self-adjoint operators.

Contribution

It presents a novel spectral theorem approach to represent elliptic type Toeplitz algebra as functions of commuting unbounded self-adjoint operators.

Findings

New spectral representation for elliptic type Toeplitz algebras

Identification of operators as functions of commuting unbounded self-adjoint operators

Enhanced understanding of the structure of Toeplitz operator algebras on the unit ball

Abstract

We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which are functions of certain collections of commuting unbounded self-adjoint operators in the Bergman space.