Noncommutative Burkholder/Rosenthal inequalities II: applications

We show norm estimates for the sum of independent random variables in noncommutative $L_p$-spaces for $1<p<\mathrm{\infty }$ 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 $2<p<\mathrm{\infty }$.