The pseudo-Daugavet property for narrow projections in Lorentz spaces (Q1397201)

For a Lorentz space \(X=L_{w,p}[0,1]\) with \(p>2\) there is a constant \(k_X > 1\) such that \(\|P\|\geq k_X\) for every projection \(P\) of \(X\) onto a nontrivial rich subspace. It is proved also that every rearrangement-invariant function space \(X\) with an absolutely continuous norm contains a complemented subspace isomorphic to \(X\) which is the range of a narrow projection and of a non-narrow one.