2020/01/17 by R. Haller, Haller, Rainis, Katriin Pirk +3
Mathematics · #46B04 #46B20 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2001.06197
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Daugavet-point (resp.~Δ-point) of a Banach space is a norm one element x for which every point in the unit ball (resp.~element x itself) is in the closed convex hull of unit ball elements that are almost at distance 2 from x. 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.~Δ-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 Δ-points in absolute sums of Banach spaces was started.