= Rademacher span is not complemented in L1
{c}
If the closed span of the <Rademacher functions> were a <complemented subspace> of $L^1(0,1)$, compose a projection with the inverse of its <l2 sequence space> parametrization. The <Grothendieck theorem for L1 to Hilbert operators> would make this map an <absolutely summing operator>. Its composition with the parametrization would make the identity on the infinite-dimensional <l2 sequence space> absolutely summing, contradicting its coordinate-vector test.
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