We study the set SNA (M, Y) of those Lipschitz maps from a (complete pointed) metric space
M to a Banach space Y which (strongly) attain their Lipschitz norm (ie the supremum …

In this article, we study the diameter two properties (D2Ps), the diametral diameter two
properties (diametral D2Ps), and the Daugavet property in Orlicz-Lorentz spaces equipped …

It is known that a Banach space has the strong diameter 2 property (ie every convex
combination of slices of the unit ball has diameter 2) if and only if the norm on its dual space …

We continue the investigation of the behaviour of octahedral norms in tensor products of
Banach spaces. First, we will prove the existence of a Banach space Y such that the injective …

We single out and study a natural class of Banach spaces–almost square Banach spaces. In
an almost square space we can find, given a finite set x 1, x 2,…, x N in the unit sphere, a …

We study Banach spaces with the property that, given a finite number of slices of the unit
ball, there exists a direction such that all these slices contain a line segment of length almost …

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 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 …

A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied.
The motivation for working with this class of subspaces is our observation that they inherit …