%0 Journal Article
%T An Analogue of Hinucin's Characterization of Infinite Divisibility for Operator-Valued Free Probability
%A John D. Williams
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1110.2691v3