The Kadeč-Pelczyński Dichotomy for the Predual of a von-Neumann Algebra

We first improve on one of Akemann′s criteria of weak compactness in the predual of a von Neumann algebra (denoted M∗). We then show that a non-reflective subspace of M∗ contains a subspace isomorphic to l1 which is complemented in M∗.