Unconditionality in spaces of smooth functions (Q1024172)

The paper deals with certain subspaces \(X\) of \(C_0(\Omega)\) or \(L_1[0,1]\). In the first case, it is shown that \(X\) embeds almost isometrically into \(c_0\) if all \(f\in X\) satisfy pointwise Lipschitz estimates. In the second case, it is shown, under suitable hypotheses involving the unconditional metric approximation property, that \(X\) is almost isometric to a weak\(^*\) closed subspace of \(\ell_1\). The author's results apply in particular to Müntz spaces.