The SOH Operator System

TL;DR

This paper investigates a natural operator system structure on Pisier's self-dual operator space, establishing its dual isomorphism with minimal cb-condition number and introducing a new tensor product for operator systems.

Contribution

It introduces a natural operator system on Pisier's self-dual space, proves its dual isomorphism with minimal cb-condition number, and develops a new tensor product for operator systems.

Findings

Operator system is completely order isomorphic to its dual.

The cb-condition number of the isomorphism is minimized.

A new tensor product on operator systems is constructed.

Abstract

In this paper we examine a natural operator system structure on Pisier's self-dual operator space. We prove that this operator system is completely order isomorphic to its dual with the cb-condition number of this isomorphism as small as possible. We examine further properties of this operator system and use it to create a new tensor product on operator systems.