Self-Dual Cone Systems and Tensor Products

TL;DR

This paper establishes the existence of self-dual tensor products for finite-dimensional convex cones and operator systems, and characterizes all functorial tensor products via minimal and maximal constructions.

Contribution

It proves that every cone system contained in its dual can be enlarged to a self-dual cone system, and explicitly describes all functorial tensor products of finite-dimensional cones and operator systems.

Findings

Existence of self-dual tensor products for finite-dimensional cones.

All functorial tensor products arise from minimal and maximal tensor products.

Every cone system contained in its dual can be enlarged to a self-dual cone system.

Abstract

We prove the existence of self-dual tensor products for finite-dimensional convex cones and operator systems. This is a consequence of a more general result: Every cone system, which is contained in its dual, can be enlarged to a self-dual cone system. Using the setup of cone systems, we further describe how all functorial tensor products of finite-dimensional cones and operator systems explicitly arise from the minimal and maximal tensor product.