Pedro Tradacete
Investigador Científico
ICMAT-CSIC
Computer-
assisted
research in
Functional
Analysis
We are a mathematics research group located in Madrid. Our work focuses on a variety of topics related to Functional Analysis: Banach lattices, phase retrieval, operator theory, convex geometry, and other problems with a clear analytic flavor. We are interested in using and developing tools to implement automated proof generation and Lean formalization to get a better understanding of the area.
Members
Alberto Salguero-Alarcón
Profesor Ayudante Doctor
UCM
David de Hevia
Profesor Ayudante Doctor
UPM
Enrique García-Sánchez
Profesor Ayudante Doctor
UCM
Eugene Bilokopytov
Postdoctoral researcher
ICMAT-CSIC
David Muñoz-Lahoz
PhD student
ICMAT-UAM
Jorge S. Ibáñez-Marcos
PhD student
UCM
Jesús Illescas Fiorito
PhD student
UCM
Nazaret Trejo-Arroyo
PhD student
UCM
Gonzalo Martínez-Fernández
PhD student
ICMAT-CSIC
Publications
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\(f\)-algebra products on AL and AM-spaces
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A universal approximation theorem and its applications to vector lattice theory
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A characterization of complex stable phase retrieval in Banach lattices
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Banach lattices of positively homogeneous functions induced by a Banach space
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Norm-attaining lattice homomorphisms and renormings of Banach lattices
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Complemented subspaces of Banach lattices
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Polyhedrality for twisted sums with \(C(\omega^\alpha)\)
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Banach lattices with upper \(p\)-estimates: free and injective objects
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Countability conditions in locally solid convergence spaces
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The strong Nakano property in Banach lattices
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Composition of locally solid convergences
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Band projections and order idempotents in Banach lattice algebras
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Extremes of interpolation scales of Banach spaces
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Banach lattice AM-algebras
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The least doubling constant of a path graph
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Atomicity of Boolean algebras and vector lattices in terms of order convergence
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Band projections in spaces of regular operators
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Free objects in Banach space theory
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Characterizations of the projection bands and some order properties of the lattices of continuous functions
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Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps
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Free dual spaces and free Banach lattices
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Order continuity and regularity on vector lattices and on lattices of continuous functions
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Locally solid convergences and order continuity of positive operators
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When Kalton and Peck met Fourier
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Free complex Banach lattices
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The complemented subspace problem for \(C(K)\)-spaces: a counterexample
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Amalgamation and injectivity in Banach lattices
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Strictly singular non-compact operators between \(L_p\) spaces
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Doubling constants and spectral theory on graphs
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Maximum modulus principle for multipliers and mean ergodic multiplication operators
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Compact spaces associated to separable Banach lattices
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On the \(A_\infty\) condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition
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Invariant subspaces for positive operators on Banach spaces with unconditional basis
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Linear versus lattice embeddings between Banach lattices
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A Godefroy-Kalton principle for free Banach lattices
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Order and uo-convergence in spaces of continuous functions
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Disjointly non-singular operators on order continuous Banach lattices complement the unbounded norm topology
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Free Banach lattices under convexity conditions
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Multiplier algebras of normed spaces of continuous functions
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On the three space property for \(C(K)\)-spaces
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Daugavet property in tensor product spaces
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Continuous valuations on the space of Lipschitz functions on the sphere
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Strictly singular multiplication operators on \(\mathcal{L} (X)\)
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Valuations on Banach lattices
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Valuations on Banach lattices
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\(p\)-regularity and weights for operators between \(L^p\)-spaces
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Sailing over three problems of Koszmider
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A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\)
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Which multiplication operators are surjective isometries?
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Strict singularity: a lattice approach
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Continuity and holomorphicity of symbols of weighted composition operators
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\((p,q)\)-regular operators between Banach lattices
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Principal minor assignment, isometries of Hilbert spaces, volumes of parallelepipeds and rescaling of sesqui-holomorphic functions
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The least doubling constant of a metric measure space
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The free Banach lattices generated by \(\ell_p\) and \(c_0\)
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Random unconditional convergence of vector-valued Dirichlet series
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The behaviour of quasi-linear maps on \(C(K)\)-spaces
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Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator
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Calderón-Lozanovskii interpolation on quasi-Banach lattices
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Continuity and representation of valuations on star bodies
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The free Banach lattice generated by a Banach space
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Almost band preservers
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Isometry invariant Finsler metrics on Hilbert spaces.
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Almost disjointness preservers
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Interpolation and extrapolation of strictly singular operators between \(L_{p}\) spaces
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Shellable weakly compact subsets of \(C[0,1]\)
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Radial continuous valuations on star bodies
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Disjointly homogeneous Banach lattices and applications
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Bartle-Dunford-Schwartz integration for positive vector measures and representation of quasi-Banach lattices
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Bases of random unconditional convergence in Banach spaces
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Strictly singular operators in pairs of \(L_p\) space
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Weakly compactly generated Banach lattices
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Optimal rearrangement invariant range for Hardy-type operators
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Banach lattice versions of strict singularity
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Best constants for the Hardy-Littlewood maximal operator on finite graphs
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Characterization of the restricted type spaces \(R(X)\)
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Positive Schur properties in spaces of regular operators
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Transitive maps on topological spaces
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Positively norming sets in Banach function spaces
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Disjointly homogeneous Banach lattices: duality and complementation
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Rearrangement invariant spaces with Kato property
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The convex hull of a Banach-Saks set
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Extrapolation on \(L^{p,\infty}({\mu})\)
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Spectral properties of disjointly strictly singular operators
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Maurey-Rosenthal factorization for \(p\)-summing operators and Dodds-Fremlin domination
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Strictly singular and power-compact operators on Banach lattices
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The invariant subspace problem in Banach spaces
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Domination problems for strictly singular operators and other related classes
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\(c_{0}\)-singular and \(\ell_{1}\)-singular operators between vector-valued Banach lattices
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Interpolation of Banach lattices and factorization of \(p\)-convex and \(q\)-concave operators
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Subspace structure of Lorentz \(L_{p,q}\) spaces and strictly singular operators
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Strictly singular operators on \(L_p\) spaces and interpolation
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Disjointly homogeneous Banach lattices and compact products of operators
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Characterizations of strictly singular operators on Banach lattices
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Powers of operators dominated by strictly singular operators
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Factorization and domination of positive Banach--Saks operators
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Invariant subspaces of positive strictly singular operators on Banach lattices
Preprints
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Free Products of Banach Lattices
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On the free Banach lattice generated by a lattice
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Lattice-ordered algebras admitting a polynomial growth continuous function calculus
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Convexity and concavity in Banach lattices
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Wickstead's conjecture on positive projections and non-representable Banach lattice algebras
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The Dedekind completion of an Archimedean ordered vector space as a reflector
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Normed lattices majorizing in their norm completions
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A Classification of Order Convergence via a Transfinite Fatou Hierarchy
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New results on Fourier multipliers on $L^p$: a perspective through unimodular symbols
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Banach lattices with upper $p$-estimates: Renorming and factorization
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Relative uniform completion of a vector lattice
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On the existence of large subspaces of $C(K)$ that perform stable phase retrieval
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Isometric embeddings into $C(K)$-spaces doing stable phase retrieval
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Non-continuous valuations on convex bodies and a new characterization of volume
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Free Banach $f$-algebras
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Coordinate systems in Banach spaces and lattices
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Derived functors associated to the ideal of compact operators in Banach spaces
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Free quasi-Banach lattices
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Minimizing measures for the doubling condition
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Disjointly non-singular operators and various topologies on Banach lattices
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Locally solid convergence structures
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A negative solution to the complemented subspace problem in Banach lattices
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Free Banach lattices
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Vector lattice approach to the Riesz and Stone Representation theorems
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Dot product invariant valuations on Lip$(S^{n-1})$
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Invariant Hermitean Metric Generated By Reproducing Kernel Hilbert Spaces
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A Jordan-like decomposition theorem for valuations on star bodies
Events
Forthcoming
Past
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Advanced Course - Ordered Vector Spaces and Their Completions
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BSBL Seminar: The phase retrieval problem (Mitchell A. Taylor)
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BSBL Seminar: Free products of Banach lattices (Gonzalo Martínez-Fernández)
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Workshop on Free Banach Lattices 2026
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BSBL Seminar: On uniform homeomorphisms on interpolation scales of Banach spaces (Valentin Ferenczi)
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BSBL Seminar: The ball fixed point property in spaces of continuous functions (Antonio Avilés)
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BSBL Seminar: On complex structures on Banach spaces, two questions of Kalton-Swanson, and uniqueness of algebra norms (Valentin Ferenczi)
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BSBL Seminar: Komlos property in Banach lattices (Wassim Dhifaoui)
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BSBL Seminar: Strongly norm attaining Lipschitz maps (Miguel Martín)
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BSBL Seminar: Interpolation of families of Banach spaces: ℓ₂ and uniform homeomorphism of spheres (Giulia Fantato)
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BSBL Seminar: Free Banach f-algebras (David Muñoz Lahoz)
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BSBL Seminar: Convexity conditions and free objects in quasi-Banach lattices (Alberto Salguero)
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BSBL Seminar: An introduction to homological algebra for Banach spacers (Nazaret Trejo)
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BSBL Seminar: Norm-attaining lattice homomorphisms (David de Hevia)
Projects
2025-2029
Banach lattices, Geometric Valuation Theory and Machine Learning
Ministerio de Ciencia e Innovación (PID2024-162214NB-I00)
The main research lines of this project focus on Banach lattices, Geometric Valuation Theory, and the mathematical foundations of Machine Learning, with particular emphasis on the interactions between Functional Analysis, Convex Geometry, lattice structures, measure theory, and high-dimensional methods. The project aims to strengthen interdisciplinary research in these areas while also exploring applications of mathematical analysis to Machine Learning, including problems with potential impact in renewable energy forecasting and related technological challenges.
2026-2027
Analysis and Applications of Order and Lattice Structures
Consejo Superior de Investigaciones Científicas (COOPB25033)
This project aims to strengthen scientific collaboration between Spanish and Tunisian researchers working in Analysis, Probability, and their applications, with a special focus on training PhD students and early-career researchers and fostering opportunities in academia and the technology sector. Building on a previous iCOOP action, the project centers on the theory of Free Banach lattices and related order structures, seeking to advance their mathematical foundations and explore applications to Mathematical Economy, Finance, and Machine Learning.
2024-2027
Operator Theory on Free Banach lattices
Bilateral grant AEI-DFG (PCI2024-155094-2).
Banach lattices provide an abstract framework for studying function spaces and order-preserving structures that appear across mathematical analysis, including partial differential equations, stochastic analysis, and dynamical systems. Free Banach lattices have opened new directions in the field by producing canonical examples with unexpected properties, but a systematic theory of positive operators on them is still missing. This project aims to develop further this theory, deepening the understanding of free Banach lattices while also using their universal properties to construct new examples and counterexamples that may help resolve longstanding questions in the general theory of positive operators.