Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Daugavet property
  • Daugavet point
  • delta-point
  • absolute sum
  • diameter two property

Mathematics Subject Classification

46B20, 46B04

References

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Suggested citation

R. Haller, K. Pirk, T. Veeorg. “Daugavet- and Delta-Points in Absolute Sums of Banach Spaces.” Journal of Convex Analysis 28 (2021), No. 1, 41–54. https://doi.org/10.68381/jca28005

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.