On weak boundary representations and quasi hyperrigidity for operator systems

Let A be a unital C-*-algebra and S be an operator system in A. It is shown that, an irreducible representation pi of A is a weak boundary representation for S if and only if its n-amplification pi((n)) is a weak boundary representation for the operator system M-n(S)for any n >= 2. Also, we deduce that the operator system S is quasi hyperrigid in A if and only if the operator system M-n(S) is quasi hyperrigid in M-n(A) any n >= 2.