In contrast to the separable case, we prove that the existence of almost L-orthogonal vectors
in a nonseparable Banach space X (octahedrality) does not imply the existence of nonzero …

We compute the Borel complexity of some classes of Banach spaces such as different
versions of diameter two properties, spaces satisfying the Daugavet equation or spaces with …

In 1989, G. Godefroy proved that a Banach space contains an isomorphic copy of ℓ1 if and
only if it can be equivalently renormed to be octahedral. It is known that octahedral norms …

We characterise those Banach spaces X which satisfy that L (Y, X) is octahedral for every
non-zero Banach space Y. They are those satisfying that, for every finite dimensional …

We show that finite dimensional Banach spaces fail to be uniformly non locally almost
square. Moreover, we construct an equivalent almost square bidual norm on ℓ∞. As a …

We prove that every Banach space admitting a Gâteaux smooth norm and containing a
complemented copy of ℓ 1 has an equivalent renorming which is simultaneously Gâteaux …

In this paper, we study octahedral norms in free Banach lattices FBL E generated by a
Banach space E. We prove that if E is an L_1 (μ) L 1 (μ)-space, a predual of von Neumann …

We continue with the study of octahedral norms in the context of spaces of Lipschitz
functions and in their duals. First, we prove that the norm of J (M)∗∗ is octahedral as soon …

Bidual octahedral renormings in Banach spaces Page 1 Bidual octahedral renormings in Banach
spaces Johann Langemets University of Tartu, Estonia April 30th, 2019 Granada, Spain Page …