Journal of Convex Analysis 28 (2021), No. 1, 041--054
Copyright Heldermann Verlag 2021
Daugavet- and Delta-Points in Absolute Sums of Banach Spaces
Rainis Haller
Institute of Mathematics and Statistics, University of Tartu, 51009 Tartu, Estonia
rainis.haller@ut.ee
Katriin Pirk
Institute of Mathematics and Statistics, University of Tartu, 51009 Tartu, Estonia
katriin.pirk@ut.ee
Triinu Veeorg
Institute of Mathematics and Statistics, University of Tartu, 51009 Tartu, Estonia
triinu.veeorg@gmail.com
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). Our results complement the ones of T.A.Abrahamsen, R.Haller, V.Lima and K.Pirk [Delta- and Daugavet-points in Banach spaces, Proc. Edinb. Math. Soc. 63/2 (2020) 475--496] concerning the existence of Daugavet- and Δ-points in absolute sums of Banach spaces.
Keywords: Daugavet property, Daugavet point, delta-point, absolute sum, diameter two property.
MSC: 46B20, 46B04.
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