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I know that $\ell_2$ is isomorphic to a subspace of $L_p(0,1)$ for any $1\le p<\infty$. However, I haven't seen anything about $L_\infty$. Is $\ell_2$ is isomorphic to a subspace of $L_\infty(0,1)$?

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    $\begingroup$ Every separable Banach space embeds into $L_{\infty}(0,1)$. $\endgroup$
    – Mateusz Wasilewski
    Commented Jun 8, 2021 at 8:45
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    $\begingroup$ Even into $C([0,1])$ (known to Banach--p. 185 in my copy of his monograph). $\endgroup$
    – bathalf15320
    Commented Jun 8, 2021 at 12:20
  • $\begingroup$ @bathalf15320 MANY Thx! $\endgroup$
    – user92646
    Commented Jun 8, 2021 at 23:09
  • $\begingroup$ @Mateusz Wasilewski Many thx $\endgroup$
    – user92646
    Commented Jun 8, 2021 at 23:09

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