The alternative Dunford-Pettis Property in the predual of a von Neumann algebra
Let A be a be a type II von Neumann algebra with predual A . We prove that A does not satisfy the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (’n) converging weakly to ’ in A with k’nk = k’k = 1 for all n 2 N and a weakly null sequence (xn) in A such that ’n(xn) 9 0. This answers a question posed in [7].