ℓ1-contractive maps on noncommutative Lp-spaces

Let $T\colon L^p({\mathcal M})\to N})$ be a bounded operator between two noncommutative $L^p$-spaces, $1\leq p<\infty$. We say that $T$ is $\ell^1$-bounded (resp. $\ell^1$-contractive) if $T\otimes I_{\ell^1}$ extends to contractive) map from $L^p({\mathcal M};\ell^1)$ into N};\ell^1)$. show Yeadon's factorization theorem for $L^p$-isometries, p\not=2 <\infty$, applies an isometry L^2({\mathcal and only $\ell^1$-contractive. also contractive automatically $\ell^1$-contractive it satisfies one of the following conditions: either $2$-positive; or separating, is, any disjoint $a,b\in M})$ (i.e. $a^*b=ab^*=0)$, images $T(a),T(b)$ are as well.