2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128911We 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 $2<p<\infty$.To appear in Isreal J; MathOperator AlgebrasFunctional AnalysisProbabilityPrimary 46L53, 46L07; Secondary, 81S25text