Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},τ)$ over a noncommutative probability space
We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},τ)$ for any noncommutative probability space $(\mathcal{M},τ)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic classification of noncommutative $L_{p,q}$-spaces are given, which extend and complement several earlier results.
math.OA↗