@misc{10481/98237,
year = {2021},
url = {https://hdl.handle.net/10481/98237},
abstract = {We prove that every separable Banach space containing
`1 can be equivalently renormed so that its bidual space is octahedral,
which answers, in the separable case, a question in Godefroy
(1989) [5]. As a direct consequence, we obtain that every dual
Banach space, with a separable predual, failing to be strongly regular
(that is, without convex combinations of slices with diameter
arbitrarily small for some closed, convex and bounded subset) can
be equivalently renormed with a dual norm to satisfy the strong diameter
two property (that is, such that every convex combination
of slices in its unit ball has diameter two).},
organization = {The work of J. Langemets was supported by the Estonian Research Council
grant (PUTJD702) and by institutional research funding IUT (IUT20-57) of the
Estonian Ministry of Education and Research.
The work of G. L opez-P erez was supported by MINECO (Spain) Grant
MTM2015-65020-P and by Junta de Andaluc  a Grant FQM-0185.},
title = {Bidual octahedral renormings and strong regularity in banach spaces},
author = {López Pérez, Ginés and Langemets, Johann},
}