Matrix regular operator space and operator system

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 $V^{\ast }$ are (nonunital) operator systems.

8 pages, to appear in JMAA