An Analogue of Hin\u{c}in's Characterization of Infinite Divisibility   for Operator-Valued Free Probability
  Let $B$ be a finite, separable von Neumann algebra. We prove that a $B$-valued distribution $\mu$ that is the weak limit of an infinitesimal array is infinitely divisible. The proof of this theorem utilizes the Steinitz lemma and may be adapted to provide a nonstandard proof of this type of theorem for various other probabilistic categories. We also develop weak topologies for this theory and prove the corresponding compactness and convergence results. 
John D. Williams
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