Israel Journal of Mathematics

, Volume 167, Issue 1, pp 227–282

Noncommutative Burkholder/Rosenthal inequalities II: Applications


DOI: 10.1007/s11856-008-1048-4

Cite this article as:
Junge, M. & Xu, Q. Isr. J. Math. (2008) 167: 227. doi:10.1007/s11856-008-1048-4


We show norm estimates for the sum of independent random variables in noncommutative Lp-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 Lp for 2 < p < ∞.

Copyright information

© Hebrew University Magnes Press 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon CedexFrance