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 …

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 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 …

It is known that a Banach space contains an isomorphic copy of $ c_0 $ if, and only if, it can
be equivalently renormed to be almost square. We introduce and study transfinite versions …

We solve some open problems regarding diameter two properties within the class of Banach
spaces of real-valued Lipschitz functions by using de Leeuw's transform. Namely, we show …

We study $ C $-rich spaces, lush spaces, and $ C $-extremely regular spaces concerning
with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform …

We prove that the Lipschitz-free space over a metric space M is locally almost square
whenever M is a length space. Consequently, the Lipschitz-free space is locally almost …

We introduce a vector-valued version of a uniform algebra, called the vector-valued function
space over a uniform algebra. The diameter two properties of the vector-valued function …

We give a characterisation of the weak⁎ symmetric strong diameter 2 property for Lipschitz
function spaces in terms of a property of the corresponding metric space. Using this …

Let $ M $ be a metric space and $ X $ be a Banach space. In this paper we address several
questions about the structure of $\mathcal F (M)\widehat {\otimes} _\pi X $ and $\mathop …