Local operator system structures and their tensor products

TL;DR

This paper develops the theory of tensor products within local operator systems, introducing minimal and maximal structures analogous to existing operator system tensor products, expanding the mathematical framework in this area.

Contribution

It introduces and analyzes minimal and maximal local operator system structures, extending the theory of tensor products in operator systems.

Findings

Defined minimal and maximal local operator system structures

Established properties and relationships of these structures

Extended tensor product theory to local operator systems

Abstract

We introduce and explore the theory of tensor products in the category of local operator systems. Analogous to minimal operator system OMIN and maximal operator system OMAX, minimal and maximal local operator system structures LOMIN and LOMAX, respectively, are also discussed.