Relative weak injectivity of operator system pairs

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 [11] proved that the C⁎-algebra C⁎(F∞) of the free group F∞ on countably many generators characterises 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⁎(F∞) also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products [9,10].