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arXiv · 0705.1952

Noncommutative Burkholder/Rosenthal inequalities II: applications

Marius Junge·Quanhua Xu
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Abstract

We show norm estimates for the sum of independent random variables in noncommutative $L_p$-spaces for $1<p<\infty$ following our previous work. These estimates generalize the classical Rosenthal inequality in the commutative case. Among 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 $2<p<\infty$.

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Marius Junge, Quanhua Xu. 2007-05-14. Noncommutative Burkholder/Rosenthal inequalities II: applications. https://arxiv.org/abs/0705.1952

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