A Δ-point x of a Banach space is a norm-one element that is arbitrarily close to convex
combinations of elements in the unit ball that are almost at distance 2 from x. If, in addition …

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 …

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 …

In this paper we study the structure of the set Hom. X; R/of all lattice homomorphisms from a
Banach lattice X into R. Using the relation among lattice homomorphisms and disjoint …

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 …

Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach
space Y is contained in a separable ideal in Y. We improve this result by replacing the term …

Abstract The category Ban of Banach spaces and linear maps of norm≤ 1 is locally ℵ 1-
presentable but not locally finitely presentable. We prove, however, that Ban is locally finitely …

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 …