Delta-points in Banach spaces generated by adequate families
Trond A. Abrahamsen, Vegard Lima, André Martiny
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Source: Crossref
Published: Sep 1, 2022
DOI: 10.1215/00192082-10123638
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We study delta-points in Banach spaces hA,p generated by adequate families A, where 1≤p<∞. When p>1, we prove that neither hA,p nor its dual contain delta-points. Under the extra assumption that A is regular, we prove that the same is true when p=1. In particular, the Schreier spaces and their duals fail to have delta-points. If A consists only of finite sets, we are able to rule out the existence of delta-points in hA,1 and Daugavet-points in its dual. We also show that if hA,1 is polyhedral, then it is either (I)-polyhedral or (V)-polyhedral (in the sense of Fonf and Veselý).
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