Amalgamated free products of commutative C*-algebras are residually finite-dimensional

TL;DR

This paper proves that the amalgamated free product of separable commutative C*-algebras always has enough finite-dimensional representations to distinguish its elements.

Contribution

It establishes that such amalgamated free products are residually finite-dimensional, a property not previously confirmed for this class of algebras.

Findings

Amalgamated free products of separable commutative C*-algebras are residually finite-dimensional.

The result extends understanding of the structure of free products in operator algebras.

Residually finite-dimensionality aids in classifying and analyzing these algebras.

Abstract

We prove that an amalgamated free product of separable commutative C*-algebras is residually finite-dimensional.