Relative weak injectivity of operator system pairs

2013/07/09 by Bhattacharya, Angshuman
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1307.2598

Abstract

The concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg \citeKr proved that the C*-algebra C^*(\mathbbf_∞) of the free group \mathbbf_∞ on countably many generators characterizes relative weak injectivity for pairs of C*-algebras by means of the maximal tensor product. One of the main results of this paper shows that C^*(\mathbbf_∞) also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products \citeKP1,KP2.

Related

• Relative Weak Injectivity for Operator Systems
• Relative Weak Injectivity for C*-algebras
• Operator system quotients of matrix algebras and their tensor products
• Super Operator Systems, Strong Norms, and Operator Tensor Products
• Tensor Products of Operator Systems