Abstract

It is known that a Banach space has the strong diameter 2 property (i.e. every convex combination of slices of the unit ball has diameter 2) if and only if the norm on its dual space is octahedral (a notion introduced by Godefroy and Maurey). We consider two more versions of octahedrality, which are dual properties to the diameter 2 property and its local version (i.e., respectively, every relatively weakly open subset and every slice of the unit ball has diameter 2). We study stability properties of different types of octahedrality, which, by duality, provide easier proofs of many known results on diameter 2 properties.

Author information

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

Rainis Haller

Institute of Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia

rainis.haller@ut.ee

Johann Langemets

Institute of Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia

johann.langemets@ut.ee

Märt Põldvere

Institute of Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia

mart.poldvere@ut.ee

Keywords

  • Diameter 2 property
  • slice
  • relatively weakly open set
  • octahedral norm

Mathematics Subject Classification

46B20, 46B22

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Suggested citation

R. Haller, J. Langemets, M. Põldvere. “On Duality of Diameter 2 Properties.” Journal of Convex Analysis 22 (2015), No. 2, 465–483. https://doi.org/10.68381/jca22021

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.