16.5. References 429The remainder of the proof is virtually identical to the proof of Proposi-
tion 3.7.11. Indeed, if A is exact, then so is A^0 P and hence exactness of the
sequence
o--+ J 0 A^0 P--+ A 0 A^0 P--+ c{(r) 0 A^0 P--+ o
would imply that the product map
c{(r) 0 A^0 P--+ JB(£^2 (r))
induced by the left and right regular representations is also min-continuous.
However, this implies r is amenable (Proposition 6.4.1), which is a contra-
diction. 0
16.5. ReferencesThis chapter evolved out of [27].