A Note on Decomposable Maps on Operator Systems

TL;DR

This paper characterizes operator systems where all positive maps are decomposable and provides a new proof of a known characterization of decomposable maps, advancing understanding in operator algebra theory.

Contribution

It offers a characterization of operator systems with universally decomposable positive maps and presents a more direct proof of Størmer's decomposition theorem.

Findings

Operator systems with all positive maps decomposable are characterized.

A new, more direct proof of Størmer's characterization of decomposable maps is provided.

The results deepen the understanding of positive maps in operator systems.

Abstract

This article contains a characterization of operator systems $\cS$ with the property that every positive map $\phi:\cS \rightarrow M_n$ is decomposable, as well as an alternate and a more direct proof of a characterization of decomposable maps due to E. St\o rmer.