Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590576 | Journal of Functional Analysis | 2014 | 12 Pages |
Abstract
We study the relation between octahedral norms, Daugavet property and the size of convex combinations of slices in Banach spaces. We prove that the norm of an arbitrary Banach space is octahedral if, and only if, every convex combination of w⁎w⁎-slices in the dual unit ball has diameter 2, which answers an open question. As a consequence we get that the Banach spaces with the Daugavet property and its dual spaces have octahedral norms. Also, we show that for every separable Banach space containing ℓ1ℓ1 and for every ε>0ε>0 there is an equivalent norm so that every convex combination of w⁎w⁎-slices in the dual unit ball has diameter at least 2−ε2−ε.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Julio Becerra Guerrero, Ginés López-Pérez, Abraham Rueda Zoca,