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].