## Operator systems and C$^*$-extreme points

### Volume 247 / 2019

Studia Mathematica 247 (2019), 45-62
MSC: Primary 46L07, 46L52, 47L07; Secondary 46L05.
DOI: 10.4064/sm170807-15-2
Published online: 5 November 2018

#### Abstract

We study operator systems over a von Neumann algebra $\mathcal {C}$ that can be represented as concrete systems of operator-valued weak$^*$ continuous ${\mathcal {C}}^{\prime }$-affine maps. In the case $\mathcal {C}={\mathbb {B}}(\mathcal {H})$ such systems are shown to be equivalent to the usual operator systems, and an application of this equivalence to C$^*$-convex sets is presented.