, Volume 167, Issue 1, pp 227-282
Date: 03 Oct 2008

Noncommutative Burkholder/Rosenthal inequalities II: Applications

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Abstract

We show norm estimates for the sum of independent random variables in noncommutative L p -spaces for 1 < p < ∞, following our previous work. These estimates generalize the classical Rosenthal inequality in the commutative case. As applications, we derive an equivalence for the p-norm of the singular values of a random matrix with independent entries, and characterize those symmetric subspaces and unitary ideals which can be realized as subspaces of a noncommutative L p for 2 < p < ∞.