A construction of inductive limit for operator system

TL;DR

This paper introduces a method for constructing inductive limits of operator systems using Archimedeanization, highlighting conditions under which nuclearity properties are preserved, though the limits may not always be closed.

Contribution

It presents a novel construction of inductive limits for operator systems via Archimedeanization, expanding understanding of their nuclearity properties.

Findings

Inductive limits may not be closed operator systems.

Nuclearity properties can be preserved under certain conditions.

The construction broadens the framework for operator system analysis.

Abstract

In this paper, we show a construction of inductive limit for operator system based on Archimedeanization. This inductive limit may be not a closed operator system. We prove that many nuclearity properties could be preserved by a special case of this inductive limit.