Dual operator systems

TL;DR

This paper characterizes dual operator systems and spaces, showing they can be represented as weak* closed subsystems of bounded operators on a Hilbert space, and provides examples of dual unital operator spaces.

Contribution

It establishes that dual operator systems and spaces can be completely isometrically and weak* homeomorphically embedded into B(H), and presents new examples of dual unital operator spaces.

Findings

Dual operator systems can be represented as weak* closed subsystems of B(H).

Dual unital operator spaces have analogous representation results.

Provides new examples of dual unital operator spaces.

Abstract

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak* homeomorphically as a weak* closed operator subsystem of $B(H)$. An analogous result is proved for unital operator spaces. Finally, we give some somewhat surprising examples of dual unital operator spaces.