The almost Daugavet property and translation-invariant subspaces

Abstract

Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group G. We show that C Λ (G) has the almost Daugavet property if and only if Λ is an infinite set, and that L 1 Λ (G) has the almost Daugavet property if and only if Λ is not a Λ(1) set.2010 Mathematics Subject Classification. Primary 46B04; secondary 43A46.