Weak compactness in the dual space of a C∗-algebra

AbstractSeveral results in noncommutative measure theory for C∗-algebras are proved. A bounded linear map from a C∗-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {ƒi} of states on a W∗-algebra converges weakly if it converges weak∗ (Corollary 3.3)