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Strong limit theorems for orthogonal sequences in von Neumann algebras. (English) Zbl 0601.46058
Let \(\phi\) be a faithful normal state on a von Neumann algebra A. It is proved that if a sequence \(\{x_ n\}\) in A is orthogonal relative to \(\phi\) and \(\sum \phi (x^*_ nx_ n)(\log n/n)^ 2\) is finite, then the sequence \(\{\) 1/n\(\sum^{n}_{k=1}x_ k\}\) of averages converges almost uniformly in A.
Reviewer: E.Azoff

MSC:
46L10 General theory of von Neumann algebras
60F15 Strong limit theorems
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