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arxiv: 2001.06197 · v1 · pith:PM47GZWHnew · submitted 2020-01-17 · 🧮 math.FA

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

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keywords banachrespdeltaelementpointspacesabsoluteball
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A Daugavet-point (resp.~$\Delta$-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.~$\Delta$-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 $\Delta$-points in absolute sums of Banach spaces was started.

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