Daugavet- and Delta-points in absolute sums of Banach spaces

preprint2020arXivOpen access

Abstract

A Daugavet-point (resp.~ΔΔ-point) of a Banach space is a norm one element xx for which every point in the unit ball (resp.~element xx itself) is in the closed convex hull of unit ball elements that are almost at distance 2 from xx. A Banach space has the well-known Daugavet property (resp.~diametral local diameter 2 property) if and only if every norm one element is a Daugavet-point (resp.~ΔΔ-point). This paper complements the article "Delta- and Daugavet-points in Banach spaces" by T. A. Abrahamsen, R. Haller, V. Lima, and K. Pirk, where the study of the existence of Daugavet- and ΔΔ-points in absolute sums of Banach spaces was started.

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