The Hyperrigidity Conjecture for Spectrahedra

TL;DR

This paper proves that for certain compact spectrahedra with closed extreme points, the associated operator system of continuous affine functions exhibits hyperrigidity within the C*-algebra of continuous functions on the extreme points.

Contribution

It establishes a hyperrigidity result for operator systems derived from spectrahedra with closed extreme points, advancing understanding in operator algebra theory.

Findings

Hyperrigidity holds for operator systems of continuous affine functions on specific spectrahedra.

The set of extreme points being closed is crucial for hyperrigidity.

The result links geometric properties of spectrahedra to algebraic rigidity properties.

Abstract

We show that if K is a compact spectrahedron whose set of extreme points is closed, then the operator system of continuous affine functions on K is hyperrigid in the C*-algebra C(ex(K)).