We introduce extensions of $\Delta $-points and Daugavet points in which slices are
replaced by relative weakly open subsets (super $\Delta $-points and super Daugavet …

The aim of this note is to study some geometrical properties like diameter two properties,
octahedrality and almost squareness in the setting of (symmetric) tensor product spaces. In …

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 F (M)⁎⁎ is octahedral as soon …

We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $ X $ of $ C
[0, 1] $ on which every weakly compact projection $ P $ satisfies the equation $\| IP\|= 1+\| P …

The aim of this note is to provide several variants of the diameter two properties for Banach
spaces. We study such properties looking for the abundance of diametral points, which …

The aim of this note is to study octahedrality in vector-valued Lipschitz-free Banach spaces
on a metric space, under topological hypotheses on it, by analysing the weak-star strong …

We study the Daugavet property in tensor products of Banach spaces. We show that-
preduals with the Daugavet property, in particular, spaces of continuous functions with this …

In this work we study three different versions of small diameter properties of the unit ball in a
Banach space and its dual. The related concepts for all closed bounded convex sets of a …

We study the unknown differences between the size of slices and relatively weakly open
subsets of the unit ball in Banach spaces. We show that every Banach space containing c 0 …

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 …