2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75197We prove that a quotient of subspace of $C_p\oplus_pR_p$ ($1\le p<2$) embeds completely isomorphically into a noncommutative $L_p$-space, where $C_p$ and $R_p$ are respectively the $p$-column and $p$-row Hilbertian operator spaces. We also represent $C_q$ and $R_q$ ($p<q\le2$) as quotients of subspaces of $C_p\oplus_pR_p$. Consequently, $C_q$ and $R_q$ embed completely isomorphically into a noncommutative $L_p(M)$. We further show that the underlying von Neumann algebra $M$ cannot be semifinite.Functional AnalysisOperator AlgebrasPrimary 46L07; Secondary 47L25text