3 problems

Blackadar–Handelman conjecture. The set

Let $A$ be a simple, unital $C^*$-algebra. Say that all ranks are realized if, for every lower-semicontinuous affine function $f\colon QT(A)\to(0,\infty]$, there exists…

Blackadar–Handelman Choquet simplex conjecture. The affine space $DF(A)$ is a Choquet simplex for any $C^*$-algebra $A$.