TY - JOUR
T1 - Noncommutative Burkholder/Rosenthal inequalities II
T2 - Applications
AU - Junge, Marius
AU - Xu, Quanhua
N1 - Funding Information:
∗ 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. Received March 8, 2007
PY - 2008/10
Y1 - 2008/10
N2 - 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 < ∞.
AB - 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 < ∞.
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U2 - 10.1007/s11856-008-1048-4
DO - 10.1007/s11856-008-1048-4
M3 - Article
AN - SCOPUS:57849107738
SN - 0021-2172
VL - 167
SP - 227
EP - 282
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -