Delta-points in Banach spaces generated by adequate families

摘要

© 2022 by the University of Illinois Urbana-Champaign.We study delta-points in Banach spaces hA;p generated by adequate families A, where (formula presented), we prove that neither hA;p nor its dual contain deltapoints. Under the extra assumption that A is regular, we prove that the same is true when p D 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).