7 problems

A separable operator system $S$ is a unital, $*$-closed subspace of a $C^*$-algebra, and a unital completely positive map has the unique extension property (u.e.p.) if every unital…

The direct sum axiom for operator spaces is not naturally expressed solely through the enriched category theory of modules. Enriched algebraic theory conjecture. There should exist…

Let $\mathcal{S}_n$ be the operator system considered above, and let $d_{\infty}(\mathcal{S}_n)$ denote its associated exactness distance. Growth conjecture. The quantity…

Let $J_3$ denote the $3\times 3$ nilpotent Jordan block, let $\mathcal{H}$ be a Hilbert space, and let $\mathcal{OS}(J_3)$ and $\mathcal{OS}(X)$ be the operator systems generated b…

Approximate-unitality conjecture. The same conclusion should hold when $S$ is “approximately unital” in a suitable sense; that is, $\overline{\iota_{S^*}^*}$ should be a complete i…

Arveson's spanning conjecture. The irreducible boundary representations, equivalently the absolute extreme points, span the free spectrahedron when $\mathcal H$ and…

Let $\mathcal{A}$ be a unital operator system, let $I(\mathcal{A})$ denote its injective envelope, and let $\mathcal{F}(\mathcal{A})$ be the operator system defined in the paper. T…