Matrix regular operator space and operator system

TL;DR

This paper explores the connection between matrix regular operator spaces and operator systems, showing that certain conditions on a space and its dual characterize their isomorphism to matrix regular operator spaces.

Contribution

It establishes a precise equivalence between matrix regular operator spaces and operator systems under specific duality conditions.

Findings

V is completely isomorphic to a matrix regular operator space iff V and V* are operator systems.

Provides a characterization linking matrix regularity and operator system structure.

Enhances understanding of the structure of matrix ordered operator spaces.

Abstract

We establish a relationship between Schreiner's matrix regular operator space and Werner's (nonunital) operator system. For a matrix ordered operator space $V$ with complete norm, we show that $V$ is completely isomorphic and complete order isomorphic to a matrix regular operator space if and only if both $V$ and its dual space $V^*$ are (nonunital) operator systems.