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 …

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 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 …

Two properties of Müntz spaces Page 1 Open Access. © 2017 Trond A. Abrahamsen et al.,
published by De Gruyter Open. This work is licensed under the Creative Commons …

We study the (possible) relation between diameter two properties and various notions of
polyhedrality. I-polyhedral spaces (being non-reflexive, M-embedded) have the strong …

We introduce and study a strict monotonicity property of the norm in solid Banach lattices of
real functions that prevents such spaces from having the local diameter two property. Then …

A Banach space (or its norm) is said to have the diameter $2 $ property (D $2 $ P in short) if
every nonempty relatively weakly open subset of its closed unit ball has diameter $2 $. We …

This thesis is devoted to the study of the geometry of Banach spaces. It is composed of three
main chapters that we will briefly describe in the present paragraph, and is directed towards …

Preliminary theory will be presented prior to each result. We begin, in Subsection 1.2. 1, by
discussing Müntz spaces, which is the focus of the two first papers,“Two properties of …