By Charles A. Akemann

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V) For each s and t, \Mpv(s,t)-(i/2sn)\\°c

5. If s and k are positive integers such that 2s

REMARK. 1 also holds in the more general case where \I/ is an affine map of a weak* closed face F of (M)i. We now briefly sketch this generalization in the case where F is a positive face. 1, part (1)) that in this case we have F = [r, s] for some projections r < s. We write 6(F, # ) = sup{\\-$(q) - *(r)||i : q - r has rank one}. 1 may be stated as follows: If M. is atomic, \£ is a non-constant, self-adjoint, affine weak* continuous map from the weak* closed face F of (,M+)i into Cn, then for each a in F there is a projection p in F that commutes with a such that ||tf(p) - *(a)|| < 5(F, tf).