Mathematics – Operator Algebras
Scientific paper
2011-10-12
Mathematics
Operator Algebras
Several revisions, excised theorems incompatible with the final form of the paper
Scientific paper
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.
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