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On complemented subspaces of $L_1[0,1]$
We construct two complemented subspaces of $L_1[0,1]$. The first has the Schur property but fails the Radon--Nikodým property. The second contains a copy of $\ell_2$ but no copy of $L_1[0,1]$. Neither space is isomorphic to a Banach lattice. This gives a negative answer to the complemented-subspace
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