Unconditionality in spaces of smooth functions

Abstract

Our main result shows that subspaces of L1([0, 1]) on which the blow-up operators act compactly are isometric to dual spaces, and their natural predual belongs to the Banach-Mazur closure of quotient spaces of \(c_0({\mathbb{N}})\). Related general results are shown for subspaces X of \({\mathcal{C}_{0}} (\Omega)\) or of reflexive Kothe function spaces, which imply that when X consists of smooth functions it embeds into a Banach space with an unconditional basis.