Stephen Montgomery-Smith, The Distribution of Non-Commutative Rademacher Series.
Math. Ann. 302, (1995), 395-416.
We give a formula for the tail of the distribution of the non-commutative Rademacher series, which generalizes the result that is already available in the commutative case. As a result, we are able to calculate the norm of these series in many rearrangement invariant spaces, generalizing work of Pisier and Rodin and Semyonov.
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