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.
We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is: if Z is a closed subspace of a separable almost Daugavet space X such that the quotient space X/Z contains no copy of ℓ 1 , then Z has the almost Daugavet property, too.2000 Mathematics Subject Classification. Primary 46B04.
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.
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