Ta. Loring et J. Spielberg, APPROXIMATION OF NORMAL ELEMENTS IN THE MULTIPLIER ALGEBRA OF AN AF C-ASTERISK-ALGEBRA, Proceedings of the American Mathematical Society, 121(4), 1994, pp. 1173-1175
It is shown that there is a simple separable AF algebra A such that M(
K x A) does not have weak (FN) and such that the generalized Berg-Weyl
von Neumann Theorem does not hold for K x A.