We characterise the octahedrality of Lipschitz-free space norm in terms of a new geometric
property of the underlying metric space. We study the metric spaces with and without this …

Abstract Using methods from Convex Analysis, for each generalized pressure function we
define an upper semi-continuous affine entropy-like map, establish an abstract variational …

We study the existence of continuous (linear) operators from the Banach spaces $\mathrm
{Lip} _0 (M) $ of Lipschitz functions on infinite metric spaces $ M $ vanishing at a …

Let $\mathrm {Lip} _0 (M) $ be the space of Lipschitz functions on a complete metric space
$(M, d) $ that vanish at a point $0\in M $. We investigate its dual $\mathrm {Lip} _0 (M) …

We analyze the relationship between Borel measures and continuous linear functionals on
the space of Lipschitz functions on a complete metric space. In particular, we describe …

We investigate a way to turn an arbitrary (usually, unbounded) metric space into a bounded
metric space in such a way that the corresponding Lipschitz-free spaces and are isomorphic …

The Lipschitz-free space F (M) has an FDD when M is a separable L 1-Banach space, or
when M⊂ R n is a somewhat regular subset. The interplay between the existence of …

Let be the space of Lipschitz functions on a complete metric space M that vanish at a base
point. We prove that every normal functional in is weak* continuous; that is, in order to verify …

Lipschitz-free spaces F (M) are canonical linearizations of arbitrary complete metric spaces
M. More specifically, F (M) is the unique Banach space that contains an isometric copy of M …

The aim of this dissertation is to analyse and solve several problems in the theory of
diameter two properties, octahedrality, and to take advantage of the strong connection …