Isomorphic classification of 𝐿_{𝑝,𝑞}-spaces: the case 𝑝=2,1≤𝑞<2

Sadovskaya, O.; Sukochev, F.

doi:10.1090/proc/14058

Isomorphic classification of $L_{p,q}$-spaces: the case $p=2,\ 1\leq q< 2$
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by O. Sadovskaya and F. Sukochev PDF

Proc. Amer. Math. Soc. 146 (2018), 3975-3984 Request permission

Abstract:

Let $1\leq q<2$. We prove that the Banach space $l_{2,q}$ (respectively, $L_{2,q}(0,\infty )$) does not isomorphically embed into the space $L_{2,q}(0,1)$ (respectively, $L_{2,q}(0,1)\oplus l_{2,q}$).

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