Boundaries, Bundles and Trace Algebras

TL;DR

This paper explores the structure of noncommutative function algebras, showing how they can be embedded into homogeneous C*-algebras, thereby advancing understanding of their properties and relationships.

Contribution

It introduces a framework for analyzing noncommutative function algebras as subalgebras of homogeneous C*-algebras, connecting different areas of operator algebra theory.

Findings

Noncommutative function algebras can be studied as subalgebras of homogeneous C*-algebras.

Provides new insights into the structure and properties of noncommutative function algebras.

Establishes a link between noncommutative functions and C*-algebra representations.

Abstract

We describe how noncommutative function algebras built from noncommutative functions in the sense of \cite{K-VV2014} may be studied as subalgebras of homogeneous $C^{*}$-algebras.