  We generalize Kirchberg's weak exactness to inclusions of C*-algebras in von
Neumann algebras and study some characterizations and permanence properties
which are similar to those of exact groups. We then consider a similar
condition to Ozawa's condition (AO) with our weak exactness and generalize
Ozawa's theorem for bi-exact groups. As a corollary, we give new examples of
prime factors.
