The Choquet boundary of an operator system

TL;DR

This paper demonstrates that all operator systems and unital operator algebras possess enough boundary representations to generate their C*-envelope, advancing the understanding of their boundary structure.

Contribution

It establishes the existence of sufficiently many boundary representations for every operator system, ensuring they generate the C*-envelope, which is a significant theoretical development.

Findings

Every operator system has enough boundary representations.

Boundary representations generate the C*-envelope.

The result applies to unital operator algebras as well.

Abstract

We show that every operator system (and hence every unital operator algebra) has sufficiently many boundary representations to generate the C*-envelope.