Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm

  • Rainis Haller Institute of Mathematics and Statistics, University of Tartu, J. Liivi 2, 50409 Tartu
  • Katriin Pirk Institute of Mathematics and Statistics, University of Tartu, J. Liivi 2, 50409 Tartu
  • Märt Põldvere Institute of Mathematics and Statistics, University of Tartu, J. Liivi 2, 50409 Tartu
Keywords: Banach space, diameter 2 property, Daugavet property, 1-sum, relatively weakly open set

Abstract

We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under 1-sums, i.e., the direct sum of two spaces with the diametral strong diameter 2 property equipped with the 1-norm has again this property.
Published
2016-06-22
Section
Articles