Operator system structures on the unital direct sum of C*-algebras

Abstract

This work is motivated by Radulescu's result on the comparison of C*-tensor norms on C*(F_n) x C*(F_n). For unital C*-algebras A and B, there are natural inclusions of A and B into their unital free product, their maximal tensor product and their minimal tensor product. These inclusions define three operator system structures on the internal sum A+B, the first of which we identify as the coproduct of A and B in the category of operator systems. Partly using ideas from quantum entanglement theory, we prove various interrelations between these three operator systems. As an application, the present results yield a significant improvement over Radulescu's bound on C*(F_n) x C*(F_n). At the same time, this tight comparison is so general that it cannot be regarded as evidence for a positive answer to the QWEP conjecture.

17 pages, to appear in Rocky Mountain J. Math

References in corpus (3)

• Connes' embedding problem and Tsirelson's problem
• Tsirelson's problem and Kirchberg's conjecture
• Factorization and dilation problems for completely positive maps on von Neumann algebras

Cited by in corpus (1)

• A Kirchberg type tensor theorem for operator systems