8 citations · 28 across the 49 of their papers we have counts for
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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 -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…
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 . 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 generated by a distributive lattice . We characterize when 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 -order convergence is known to be ${\bf Δ}^1_…
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 -estimates: Renorming and factorization
Enrique García-Sánchez, Denny H. Leung, Mitchell A. Taylor +1
The notions of -convexity and concavity are fundamental tools for studying Banach lattices, as they partition the class of Banach lattices into a scale of spaces with -like…