P. Tradacete

Order closure, order adherence and Fatou norms

A. Avilés, M. A. Taylor, P. Tradacete

We record two results in the theory of vector and Banach lattices related to order adherence. First, we give a negative answer to Gao and Leung's question on whether the $u o$ -adher…

Aliprantis's questions on locally solid topologies

David Muñoz-Lahoz, Mitchell A. Taylor, Pedro Tradacete

In 1974, C. D. Aliprantis posed several questions concerning topological completions of locally solid vector lattices. We answer all of them in the negative. We construct Hausdorff…

Banach lattices and phase retrieval: A case study for the use of AI in mathematics

Jaume de Dios Pont, Lukas Liehr, David Muñoz-Lahoz +2

The ability of large language models to assist professional mathematicians has been progressing rapidly. Earlier this year, a group of researchers in Banach lattice theory and phas…

math.MG2026

Measure-valued valuations on star bodies

Jorge S. Ibáñez-Marcos, Monika Ludwig, Pedro Tradacete +1

A complete classification of weak $^{*}$ ~continuous, measure-valued valuations is established on star bodies in $R^{n}$ . Consequences are an integral representation of rotation equivar…

Free Products of Banach Lattices

Gonzalo Martínez-Fernández, Pedro Tradacete

We study free products, that is, coproducts, in the category of Banach lattices and contractive lattice homomorphisms. We give a concrete construction of the free product of an arb…

On the free Banach lattice generated by a lattice

Asma Ben Rjeb, Pedro Tradacete

We study structural properties of the free Banach lattice $F B L ⟨ L ⟩$ generated by a distributive lattice $L$ . We characterize when $F B L ⟨ L ⟩$ has a strong uni…

A Classification of Order Convergence via a Transfinite Fatou Hierarchy

Antonio Avilés, Christian Rosendal, Mitchell A. Taylor +1

We investigate the descriptive complexity of order convergence in separable Banach lattices. While uniform convergence is Borel and $σ$ -order convergence is known to be ${\bf Δ}^1_…

math.MG2026

Non-continuous valuations on convex bodies and a new characterization of volume

Jorge S. Ibáñez Marcos, Pedro Tradacete, Ignacio Villanueva

This paper investigates the use of automatic continuity techniques in the context of valuations on convex bodies. We first provide an automatic continuity theorem for valuations re…

Banach lattices with upper $p$ -estimates: Renorming and factorization

Enrique García-Sánchez, Denny H. Leung, Mitchell A. Taylor +1

The notions of $p$ -convexity and concavity are fundamental tools for studying Banach lattices, as they partition the class of Banach lattices into a scale of spaces with $L_{p}$ -like…

Free quasi-Banach lattices

Alberto Salguero-Alarcón, Pedro Tradacete, Nazaret Trejo-Arroyo

We study different versions of \emph{free objects} in the setting of quasi-Banach spaces and quasi-Banach lattices. Special attention is devoted to the free $p$ -convex $p$ -Banach l…

Free Banach $f$ -algebras

David Muñoz-Lahoz, Pedro Tradacete

We construct and analyze the free Banach $f$ -algebra $FB f A [E]$ generated by a Banach space $E$ , extending recent developments on free Banach lattices to the…

math.CA2025

Minimizing measures for the doubling condition

Fernando Benito F. de la Cigoña, José M. Conde Alonso, Federico Cabrera Linares +1

We study those measures whose doubling constant is the least possible among doubling measures on a given metric space. It is shown that such measures exist on every complete metric…

Complemented subspaces of Banach lattices

David de Hevia, Pedro Tradacete

We survey recent developments on the structure of complemented subspaces of Banach lattices, including in particular the construction of a complemented subspace of a $C (K)$ -space w…

Norm-attaining lattice homomorphisms and renormings of Banach lattices

Eugene Bilokopytov, Enrique García-Sánchez, David de Hevia +2

A well-known theorem due to R. C. James states that a Banach space is reflexive if and only if every bounded linear functional attains its norm. In this note we study Banach lattic…

Banach lattice AM-algebras

David Muñoz-Lahoz, Pedro Tradacete

An analogue of Kakutani's representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of $C(K)…

math.FA2024★ 1 cited

Coordinate systems in Banach spaces and lattices

Antonio Avilés, Christian Rosendal, Mitchell A. Taylor +1

Using methods of descriptive set theory, in particular, the determinacy of infinite games of perfect information, we answer several questions from the literature regarding differen…

Extremes of interpolation scales of Banach spaces

Willian Corrêa, Valentin Ferenczi, Rafela Gesing +1

M. Daher gave conditions so that the spheres of the spaces in the interior of a complex interpolation scale are uniformly homeomorphic. We look for sufficient conditions for the va…

Banach lattices of positively homogeneous functions induced by a Banach space

Niels Jakob Laustsen, Pedro Tradacete

Motivated by the construction of the free Banach lattice generated by a Banach space, we introduce and study several vector and Banach lattices of positively homogeneous functions…

math.FA2024★ 4 cited

Banach lattices with upper $p$ -estimates: free and injective objects

E. García-Sánchez, D. H. Leung, M. A. Taylor +1

We study the free Banach lattice $F B L^{(p, \infty)} [E]$ with upper $p$ -estimates generated by a Banach space $E$ . Using a classical result of Pisier on factorization through $L^{p,\…