Symmetric Strong Diameter Two Property

  • Rainis Haller
  • Johann LangemetsEmail author
  • Vegard Lima
  • Rihhard Nadel


We study Banach spaces with the property that, given a finite number of slices of the unit ball, there exists a direction such that all these slices contain a line segment of length almost 2 in this direction. This property was recently named the symmetric strong diameter two property by Abrahamsen, Nygaard, and Põldvere. The symmetric strong diameter two property is not just formally stronger than the strong diameter two property (finite convex combinations of slices have diameter 2). We show that the symmetric strong diameter two property is only preserved by \(\ell _\infty \)-sums, and working with weak star slices we show that \(\text {Lip}_0(M)\) have the weak star version of the property for several classes of metric spaces M.


Strong diameter two property almost square spaces Lipschitz spaces 

Mathematics Subject Classification

Primary 46B20 46B22 



The authors wish to express their thanks to Indrek Zolk for his collaboration in proving Lemma 5.4


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Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TartuTartuEstonia
  2. 2.NTNU, Norwegian University of Science and TechnologyÅlesundNorway
  3. 3.Department of Engineering SciencesUniversity of AgderKristiansandNorway

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