2 problems

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The complemented subspace conjecture for $L_1[0,1]$
Complemented subspace conjecture. Every complemented subspace of $L_1[0,1]$ is isomorphic either to $\ell_1$ or to $L_1[0,1]$ .
Conjectureopenbanach-spaces complemented-subspaces functional-analysisarXiv posted 2 days ago
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Existence of uncomplemented Hilbert subspaces in $L_p$ for $1\leq p<2$
Uncomplemented Hilbert-subspace conjecture. For every $p\in[1,2)$ , the space $L_p$ contains an uncomplemented subspace $W$ isomorphic to $l_2$ .
Conjecturesolvedbanach-spaces complemented-subspaces function-spacesarXiv posted 2 days ago

The complemented subspace conjecture for L1[0,1]L_1[0,1]L1​[0,1]