Containment problems for polytopes and spectrahedra appear in various applications, such
as linear and semidefinite programming, combinatorics, convexity, and stability analysis of …

For every convex body K⊆ R d, there is a minimal matrix convex set W min (K), and a
maximal matrix convex set W max (K), which have K as their ground level. We aim to find the …

In this work, we investigate measurement incompatibility in general probabilistic theories
(GPTs). We show several equivalent characterizations of compatible measurements. The …

In this work, we investigate the joint measurability of quantum effects and connect it to the
study of free spectrahedra. Free spectrahedra typically arise as matricial relaxations of linear …

A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction
by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly …

Dilation theory is a paradigm for studying operators by way of exhibiting an operator as a
compression of another operator which is in some sense well behaved. For example, every …

For matrix convex sets, a unified geometric interpretation of notions of extreme points and of
Arveson boundary points is given. These notions include, in increasing order of strength, the …

An operator $ C $ on a Hilbert space $\mathcal H $ dilates to an operator $ T $ on a Hilbert
space $\mathcal K $ if there is an isometry $ V:\mathcal H\to\mathcal K $ such that $ C= V …

A rational function belongs to the Hardy space, $ H^ 2$, of square-summable power series if
and only if it is bounded in the complex unit disk. Any such rational function is necessarily …

The purpose of this paper is to give a self-contained overview of the theory of matrix convex
sets and free spectrahedra. We will give new proofs and generalizations of key theorems …