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 (in "An alternative
Dunford-Pettis property", Studia Math. 1997),
i.e., there is a sequence (fn) converging weakly to
f in A* with |fn| =|f| =1 for
all n and a weakly null sequence (xn) in A such
that fn (xn) does not converge to 0. This answers a
question posed by Freedman.
Miguel Martín <mmartins@ugr.es>
Antonio M. Peralta <aperalta@ugr.es>