Dual operator systems

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.

10 pages

References in corpus (2)

• A double commutant theorem for operator algebras
• Metric characterizations of isometries and of unital operator spaces and systems

Cited by in corpus (4)

• Norms and Cones in the Theory of Quantum Entanglement
• Ideals and structure of operator algebras
• Weak* continuous states on Banach algebras
• Operator system structures and extensions of Schur multipliers