Descriptive complexity of diameter 2 properties
I Encuentro IMAG (20-21 marzo 2024, Granada) [POSTER]
Methods in Banach spaces (11-14 junio 2024, Badajoz)
New perspectives in Banach spaces and Banach Lattices (8-12 julio 2024, Castro Urdiales)
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 an octahedral norm. In most of the above cases our computation is even optimal, which completes the research done during the last years around this topic for isomorphism classes of Banach spaces.
Radio grande versus diámetro pequeño
IMAG Functional Analysis Seminar (31 octubre 2025, Granada)
En este seminario construiremos un ejemplo de un espacio de Banach donde todos los abiertos débiles de su bola unidad tienen radio 1, el máximo posible, pero en el cuál existen slices de su bola unidad de diámetro arbitrariamente cercano a uno. (Referencias)
Projective characterizations of Lindenstrauss and Gurariĭ spaces
7th Bringing Young Mathematicians Together Conference (17-20 noviembre 2025, Sevilla)
The Hahn-Banach theorem is a cornerstone of Functional Analysis and the search for a vector-valued version of this result leads to the concept of injective Banach spaces. However, this class is quite restrictive. To extend the theory to a broader context, one can consider two other classes of Banach spaces whose extension properties are related to finite-rank operators: \(L_1\) preduals and Gurariĭ spaces. These classes can be characterized by specific projective properties involving the classical notion of ideal and its (almost) isometric counterpart, respectively.
Well-established generalizations of \(L_1\) preduals and Gurariĭ spaces exist, namely \(\kappa\) injective spaces and spaces of (almost) universal disposition. A natural question is whether these broader classes can also be described by analogous projective properties. The answer is affirmative and leads to the development of transfinite versions of the concepts of (almost isometric) ideals.
In this talk, we will describe these new transfinite notions and explain how they characterize the corresponding classes of generalized \(L_1\) preduals and Gurariĭ spaces. Furthermore, we will present constructions of examples that fall outside these classical types, which were the original motivation for this new framework.
Big radius versus small diameter
53rd Winter School in Abstract Analysis (10-17 enero 2026, Vlachovice – Sykovec, República Checa)
In this talk we constuct an example of a Banach space where every realatively weakly open subset of its unit ball has radius 1, the maximum possible, but in which there exists slices of its unit ball with diameter arbitrarilly close to one.
(References)
ADENDA: Como me señalaron en el correspondiente congreso, el cuerpo de la página 26 no es convexo, pero \(c_0\) no es un plano de \(\mathbb{R}^2\) y nadie se queja por ello :) Las ilustraciones son solo eso, ilustrativas (aunque podría haberlo hecho convexo, pero que le vamos a hacer).