Banach Embedding Properties of Non-Commutative $L^p$-Spaces

Let $\mathcal N$ and $\mathcal M$ be von Neumann algebras. It is proved that $L DEGREESp(\mathcal N)$ does not linearly topologically embed in $L DEGREESp(\mathcal M)$ for $\mathcal N$ infinite, $\mathcal M$ finit