Noncommutative Burkholder/Rosenthal inequalities II: Applications |
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Authors: | Marius Junge Quanhua Xu |
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Institution: | 1.Department of Mathematics,University of Illinois,Urbana,USA;2.Laboratoire de Mathématiques,Université de Franche-Comté,Besan?on Cedex,France |
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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 < ∞.
The first author is partially supported by the National Science Foundation DMS-0301116.
The second author is partially supported by the Agence Nationale de Recherche 06-BLAN-0015. |
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Keywords: | |
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