2010/11/30 by Tobias Fritz
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Operator (biology) #Product (mathematics) #Quantum #Quantum entanglement #Spectral Theory in Mathematical Physics #Tensor (intrinsic definition) #Tensor product #Unital #math-ph #math.MP #math.OA #msc:46L06 #msc:46L07 #msc:81P40
paper · pdf · doi:10.1216/rmj-2014-44-3-913
published as Rocky Mountain J. Math. 44(3), 913-936 (2014) · 17 pages, to appear in Rocky Mountain J. Math
arxiv created 2012/02/09 · openalex publication_date 2014/06/01 · arxiv updated 2014/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
This work is motivated by R\uadulescu's result~\citeR˘ad04 on the comparison of C^*-tensor norms on C^*(\Fn)⊗ C^*(\Fn). For unital C^*-algebras A and B, there are natural inclusions of A and B into the unital free product A∗1 B, the maximal tensor product A⊗max B and the minimal tensor product A⊗min B. These inclusions define three operator system structures on the internal sum A+B. 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 R\uadulescu's bound. At the same time, this tight comparison is so general that it cannot be regarded as evidence for the QWEP conjecture.