5 problems

Let $A$ be a unital $C^*$-algebra. Define the classical Cuntz semigroup $\mathrm{W}(A)$ from positive elements in $M_\infty(A)$, and let $\mathrm{DF}(A)$ be the set of normalized d…

Let $A$ be a unital, separable, nuclear ${\rm C}^*$-algebra of real rank zero and stable rank one, and let $\underline{\mathrm{Cu}}_u(A)$ denote its total Cuntz semigroup invariant…

Let $A$ be a stably finite unital C-algebra and let $X$ be a compact metric space. The radius of comparison, denoted by ${\operatorname{rc}}$, measures comparison in the Cuntz semi…

Blackadar–Handelman density conjecture. The set $LDF(A)$ is dense in $DF(A)$.

Let $A$ be a $\mathcal{Z}$-stable $C^*$-algebra, meaning that $A\cong A\otimes\mathcal{Z}$. Let $\operatorname{Cu}(A)$ be its Cuntz semigroup, and recall that a positively ordered…