Super Operator Systems, Strong Norms, and Operator Tensor Products

2012/06/29 by Ulrich Haag, Haag, Ulrich
Mathematics · #46L07 #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1206.6970

openalex publication_date 2012/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some Hilbert space. They can nevertheless be represented by bounded operators on a standard Z₂-graded Hilbert space equipped with a superinvolution. We apply this theory to investigate on the relation between certain tensor products defined for operator spaces and C^*-algebras, such as the projective tensor product, the Haagerup tensor product and the maximal C^*-tensor product.

Related

• Tensor Products of Operator Systems
• On maximal tensor products and quotient maps of operator systems
• Two Characterizations of the Maximal Tensor Product of Operator Systems
• Schur tensor product of operator spaces
• Operator space tensor norms