Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group Ĝ. We show that has the almost Daugavet property if and only if Λ is an infinite set, and that has the almost Daugavet property if and only if Λ is not a Λ(1) set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-1, author = {Simon L\"ucking}, title = {The almost Daugavet property and translation-invariant subspaces}, journal = {Colloquium Mathematicae}, volume = {135}, year = {2014}, pages = {151-163}, zbl = {1312.46016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-1} }
Simon Lücking. The almost Daugavet property and translation-invariant subspaces. Colloquium Mathematicae, Tome 135 (2014) pp. 151-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-1/