Pedro Tradacete

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About Me

I am a researcher in Mathematics at Instituto de Ciencias Matemáticas - CSIC.

Pedro Tradacete

I got my PhD from Universidad Complutense de Madrid in 2009. In 2010, I moved to Universidad de Barcelona as Juan de la Cierva Postdoc Researcher working at the Group of Real and Functional Analysis. After two years there, I came back to Madrid where I have been lecturing as Profesor Ayudante Doctor at Universidad Carlos III de Madrid until 2018, when I became Investigador Distinguido at ICMAT.

My Research interests

I am mainly interested in lattice and ordered structures in analysis and their application to other areas such as metric geometry. In particular, my research deals with the following topics:

  • Functional Analysis: Banach lattices, Banach spaces.
  • Geometric Valuation theory.
  • Operator Theory: Positive operators, interpolation theory, invariant subspaces.
  • Analysis in metric spaces: doubling measures, graph theory.








Cups of Coffee

Recent and forthcoming

Conferences or events I have been, will be or wish I could be.

Research papers

  • ALL
  • Banach spaces
  • Banach lattices
  • Positive operators
  • Strictly singular operators
  • Lp spaces
  • Rearrangement invariant spaces
  • Valuations
  • Interpolation/extrapolation
  • Graphs
  • Geometric measure theory
E. García-Sánchez, D. H. Leung, M. A. Taylor, P. Tradacete: Banach lattices with upper p-estimates: free and injective objects.
Y. Azouzi, A. Ben Rjeb, P. Tradacete: The strong Nakano property in Banach lattices.
D. de Hevia, G. Martínez-Cervantes, A. Salguero-Alarcón, P. Tradacete: A counterexample to the complemented subspace problem in Banach lattices.
D. Muñoz-Lahoz, P. Tradacete: Band projections in spaces of regular operators. Trans. Amer. Math. Soc (to appear)
E. García-Sánchez, D. de Hevia, P. Tradacete: Free objects in Banach space theory. Proceedings Biennial Conference of the Spanish Royal Mathematical Society 2022. RSME-Springer. (to appear)
T. Oikhberg, M.A. Taylor, P. Tradacete, V.G. Troitsky: Free Banach lattices. J. Eur. Math. Soc. (JEMS) (to appear)
E. Durand-Cartagena, J. Soria, P. Tradacete: The least doubling constant of a path graph. Kyoto J. Math. (to appear)
A. Avilés, G. Martínez-Cervantes, A. Rueda Zoca, P. Tradacete: Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps. Rev. Mat. Iberoamericana 40 (2024), no. 1, 189-200
E. García-Sánchez, P. Tradacete: Free dual spaces and free Banach lattices. J. Math. Anal. Appl. 532 (2024), no. 2, Paper No. 127931.
E. Durand-Cartagena, J. Soria, P. Tradacete: Doubling constants and spectral theory on graphs. Discrete Math. 346 (2023), no. 6, Paper No. 113354.
D. de Hevia, P. Tradacete: Free complex Banach lattices. J. Funct. Anal. 284 (2023), no. 10, Paper No. 109888.
F. L. Hernández, E. M. Semenov, P. Tradacete: Strictly singular non-compact operators between Lp spaces. Rev. Mat. Iberoamericana 39 (2023), no. 1, 181--200.
A. Avilés, P. Tradacete: Amalgamation and injectivity in Banach lattices. Int. Math. Res. Not. IMRN 2023, no. 2, 956-997.
E. A. Gallardo-Gutiérrez, J. González-Doña, P. Tradacete: Invariant subspaces for positive operators on Banach spaces with unconditional basis. Proc. Amer. Math. Soc. 150 (2022), no. 12, 5231-5242.
A. Avilés, G. Martínez-Cervantes, A. Rueda Zoca, P. Tradacete: Compact spaces associated to separable Banach lattices. Banach J. Math. Anal. 16 (2022), no. 4, 67.
A. Avilés, G. Martínez-Cervantes, A. Rueda Zoca, P. Tradacete: Linear versus lattice embeddings between Banach lattices. Adv. Math. 406 (2022), Paper No. 108574, 14 pp.
M. Cao, O. Domínguez, J. M. Martell, P. Tradacete: On the A condition for elliptic operators in 1-sided NTA domains satisfying the capacity density condition. Forum Math Sigma 10 (2022), Paper No. e59.
A. Avilés, G. Martínez-Cervantes, J. Rodríguez, P. Tradacete: A Godefroy-Kalton principle for free Banach lattices. Israel J. Math. 247 (2022), no. 1, 433-458.
H. Jardón-Sánchez, N. J. Laustsen, M. A. Taylor, P. Tradacete, V. G. Troitsky: Free Banach lattices under convexity conditions. RACSAM 116 (2022), No. 1, Paper No. 15, 25 p.
A. Rueda Zoca, P. Tradacete, I. Villanueva: Daugavet property in tensor product spaces. J. Inst. Math. Jussieu 20 (2021), no. 4, 1409-1428.
A. Colesanti, D. Pagnini, P. Tradacete, I. Villanueva: Continuous valuations on the space of Lipschitz functions on the sphere. J. Funct. Anal. 280 (2021), no. 4, 108873, 43 pp.
M. Mathieu, P. Tradacete: Strictly singular multiplication operators on L(X). Israel J. Math. 236 (2020), 685-709.
A. Colesanti, D. Pagnini, P. Tradacete, I. Villanueva: A class of invariant valuations on Lip(Sn-1). Adv. Math. 366 (2020), 107069.
E. A. Sánchez-Pérez, P. Tradacete: p-regularity and weights for operators between Lp spaces. Z. Anal. Anwend. 39 (2020), no. 1, 41-65.
P. Tradacete, I. Villanueva: Valuations on Banach lattices. Int. Math. Res. Not. IMRN 2020, no. 1, 287-319.
D. Carando, F. Marceca, M. Scotti, P. Tradacete: Random unconditional convergence of vector-valued Dirichlet series. J. Funct. Anal. 277 (2019), no. 9, 3156-3178.
J. Soria, P. Tradacete: The least doubling constant of a metric measure space. Ann. Acad. Sci. Fenn. Math. 44 (2019), 1015-1030.
A. Avilés, P. Tradacete, I. Villanueva: The free Banach lattices generated by lp and c0. Rev. Mat. Complutense 32 (2019), no. 2, 353-364.
E. A. Sánchez-Pérez, P. Tradacete: (p,q)-regular operators between Banach lattices. Monatsh. Math. 188 (2019), no. 2, 321-350.
J. Soria, P. Tradacete: Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator. Journal d'Analyse Mathématique 137 (2019), no. 2, 913-937.
J. Flores, F. L. Hernández, P. Tradacete: Strict singularity: a lattice approach. Positivity and Noncommutative Analysis, Trends Math., Birkäuser (2019), 153--165.
A. Avilés, J. Rodríguez, P. Tradacete: The free Banach lattice generated by a Banach space. J. Funct. Anal. 274 (2018), no. 10, 2955-2977.
Y. Raynaud, P. Tradacete: Calderón-Lozanovskii interpolation on quasi-Banach lattices. Banach J. Math. Anal. 12 (2018), no. 2, 294-313.
P. Tradacete, I. Villanueva: Continuity and representation of valuations on star bodies. Adv. Math. 329 (2018), 361-391.
F. L. Hernández, E. M. Semenov, P. Tradacete: Interpolation and extrapolation of strictly singular operators between Lp spaces. Adv. Math. 316 (2017), 667-690.
J. López-Abad, P. Tradacete: Shellable weakly compact subsets of C[0,1]. Math. Ann. 367 (2017), no. 3-4, 1777-1790.
T. Oikhberg, P. Tradacete: Almost band preservers. Positivity 21 (2017), no. 4, 1393-1423.
T. Oikhberg, P. Tradacete: Almost disjointness preservers. Canad. J. Math. 69 (2017), no. 3, 650-686.
P. Tradacete, I. Villanueva: Radial continuous valuations on star bodies. J. Math. Anal. Appl. 454 (2017), no. 2, 995-1018.
A. Avilés, A. J. Guirao, S. Lajara, J. Rodríguez, P. Tradacete: Weakly compactly generated Banach lattices. Studia Math. 234 (2016), 165-183.
J. Flores, F. L. Hernández, P. Tradacete: Disjointly homogeneous Banach lattices and applications. Ordered Structures and Applications: Positivity VII. Springer, Trends in Mathematics, 179-201 (2016).
J. Flores, J. López-Abad, P. Tradacete: Banach lattice versions of strict singularity. J. Funct. Anal. 270 (2016), 2715-2731.
J. López-Abad, P. Tradacete: Bases of random unconditional convergence in Banach spaces. Trans. Amer. Math. Soc. 368 (2016), 9001-9032.
E. A. Sánchez-Pérez, P. Tradacete: Bartle-Dunford-Schwartz integration for positive vector measures and representation of quasi-Banach lattices. J. Nonlinear Convex Anal. 17 (2016), no 2, 387-402.
E. M. Semenov, P. Tradacete, F. L. Hernández: Strictly singular operators on pairs of Lp spaces. Dokl. Math. 94 (2016), 450-452.
J. Soria, P. Tradacete: Best constants for the Hardy-Littlewood maximal operator on finite graphs. J. Math. Anal. Appl. 436 (2016), 661-682.
J. Soria, P. Tradacete: Optimal rearrangement invariant range for Hardy type operators. Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), no. 4, 865-893.
J. Soria, P. Tradacete: Characterization of the restricted type spaces R(X). Math. Inequal. Appl. 18 (2015), 295-319.
P. Tradacete: Positive Schur properties in spaces of regular operators. Positivity 19 (2015), no 2, 305-316.
F. L. Hernández, E. M. Semenov, P. Tradacete: Rearrangement invariant spaces with Kato property. Funct. Approx. Comment. Math. 50 (2014), no 2, 215-232.
J. Flores, F. L. Hernández, E. Spinu, P. Tradacete, V. G. Troitsky: Disjointly homogeneous Banach lattices: duality and complementation. J. Funct. Anal. 266 (2014), 5858-5885.
J. López-Abad, C. Ruiz, P. Tradacete: The convex hull of a Banach-Saks set. J. Funct. Anal. 266 (2014), 2251-2280.
E. A. Sánchez-Pérez, P. Tradacete: Positively norming sets in Banach function spaces. Q. J. Math. 65 (2014), 1049-1068.
M. J. Carro, P. Tradacete: Extrapolation on Lp,∞(μ). J. Funct. Anal. 265 (2013), 1840-1869.
P. Tradacete: Spectral properties of disjointly strictly singular operators, J. Math. Anal. Appl. 395 (2012), 376-384.
C. Palazuelos, E. A. Sánchez-Pérez, P. Tradacete: Maurey-Rosenthal factorization for p-summing operators and Dodds-Fremlin domination, J. Operator Theory 68 (2012), 205-222.
J. Flores, F.L. Hernández, E.M. Semenov, P. Tradacete: Strictly singular and power-compact operators on Banach lattices, Israel J. Math 188 (2012), 323-352.
J. Flores, F. L. Hernández, P. Tradacete: Domination problems for strictly singular operators and other related classes, Positivity 15 (2011), 595-616.
P. Tradacete: c0-singular and l1-singular operators between vector-valued Banach lattices, Positivity 15 (2011), 241-251.
P. Tradacete: Subspace structure of Lorentz Lpq spaces and strictly singular operators, J. Math. Anal. Appl. 367 (2010), 98-107.
Y. Raynaud, P. Tradacete: Interpolation of Banach lattices and factorization of p-convex and q-concave operators, Integral Equations Operator Theory 66 (2010), 79-112.
F.L. Hernández, E. M. Semenov, P. Tradacete: Strictly singular operators on Lp spaces and interpolation, Proc. Amer. Math. Soc. 138 (2010), 675-686.
J. Flores, P. Tradacete, V.G. Troitsky: Disjointly homogeneous Banach lattices and compact products of operators, J. Math. Anal. Appl. 354 (2009), 657-663.
J. Flores, F.L. Hernández, N.J. Kalton, P. Tradacete: Characterizations of strictly singular operators on Banach lattices, J. London Math. Soc. 79 (2009), 612-630.
J. Flores, P. Tradacete: Factorization and domination of positive Banach-Saks operators, Studia Math. 189 (2008), 91-101.
J. Flores, P. Tradacete, V.G. Troitsky: Invariant subspaces of positive strictly singular operators on Banach lattices, J. Math. Anal. Appl. 343 (2008), 743-751.
J. Flores, F.L. Hernández, P. Tradacete: Powers of operators dominated by strictly singular operators, Q. J. Math. 59 (2008), 321-334.


  • Recent progress in Banach lattices. Positivity XI, University of Ljubljana, Slovenia. July 2023.
  • Classic flavors in Banach lattice theory. Brazilian Workshop in Banach Spaces, Universidade de São Paulo, Brazil. December 2022.
  • Ret\'iculos de Banach: Cómo tener orden puede cambiarlo todo. II Encuentro Conjunto RSME-UMA, Málaga, Spain. December 2022.
  • Free Banach lattices. Conference on ordered structures with applications in economy and finance, Tunisia. May 2021.
  • Banach lattices in convex geometry. 2nd Brazilian Workshop in Geometry of Banach spaces, Ubatuba, Brazil. August 2018. slides
  • Free Banach lattices (minicourse at BIRS Oaxaca, Mexico, May 2018). Watch the videos! part 1 part 2 part 3
  • Retículos libres y un problema de Joe Diestel. XII EITA, Panticosa. October 2017.
  • Weak compactness in Banach lattices. Positivity IX, University of Alberta. July 2017. slides
  • Valuations on star sets and star bodies. RSME 2017, Functional Analysis session. Universidad de Zaragoza, February, 2017.
  • Weakly compact sets in C[0,1]. XII Encuentro de la red de Análisis Funcional y Aplicaciones. Universidad de Extremadura, March, 2016.
  • Research term Lattice Structures in Analysis and Applications, ICMAT, April-June 2024. website
  • CIMPA School Ordered structures and their applications, Tunisia, June 2024. website
  • ICMAT-IMAG Doc-course in Functional Analysis, Madrid-Granada, June 2023. website
  • Workshop Geometric Valuation Theory -- from convex sets to functions, CIEM, Castro-Urdiales, June 2023. website
  • BIRS workshop Recent advances in Banach lattices, Banff, Canada, May 2023. website
  • Workshop on Banach spaces and Banach lattices II, ICMAT, May 2022. website
  • ICMAT Postdoc Presentation Days, 22 October and 5 November 2021.
  • Workshop on Banach spaces and Banach lattices, ICMAT, September 2019. website
  • Workshop on Operators and Banach lattices II, Universidad Complutense de Madrid, November 2016. website
  • 1st Joint Meeting Brazil-Spain in Mathematics (special session: Banach spaces and set theory in interaction), Fortaleza, Brazil, December 2015.
  • RSME Conference 2015 (Functional Analysis special session), Universidad de Granada, February 2015.
  • 2nd RSME Young Researchers Conference (Functional Analysis special session), Universidad de Sevilla, September 2013.
  • Workshop on Operators and Banach lattices, Universidad Complutense de Madrid, October 2012. website
  • Jornadas RSME: The Millenium Problems, Universidad de Barcelona, June 2011. website
  • Positivity VI, El Escorial, July 2009.
  • Charla para IES: ¿Cómo encuentra Google la página web que buscas? (2022-2024)
  • P. Tradacete: Del metateatro a los fundamentos de las matemáticas, en El País (10/5/2021).
  • P. Tradacete, I. Villanueva: La medida de todas las cosas, en El País (14/7/2020).
  • P. Tradacete: Brook Taylor, músico, pintor, jurista y gran matemático, en El País (7/9/2017).
  • P. Tradacete: El problema del subespacio invariante en espacios de Banach, La Gaceta de la RSME, 14, no. 3 (2011), 491-509.
  • Universidad Carlos III de Madrid:
    • Análisis Real y Complejo, Master in Mathematical Engineering (2014/15, 2015/16, 2016/17).
    • Matemática Discreta, Master in Mathematical Engineering (2017/18).
    • Calculus II (Mechanical Engineering et al., 2011/12, 2012/13, 2013/14, 2014/15, 2015/16).
    • Calculus I (Mechanical Engineering et al., 2015/16, 2016/17, 2017/18).
    • Curso 0 matemáticas: Polinomios y desigualdades algebraicas.
  • Universidad de Barcelona:
    • Introducción al Cálculo Diferencial (2010/2011)
    • Introducción al Cálculo Integral (2010/2011)
  • Universidad Complutense de Madrid:
    • Análisis Complejo (2006/2007)
    • Análisis de Variable Real (2007/2008)
  • Problemas resueltos de estructuras algebraicas: Grupos, Anillos y Cuerpos (2010), Ed. Bubok Publishing.
  • Inverting the roles in tutoring: a collaborative learning experience in first course of mathematics, Edulearn11 proceedings, Barcelona (2011).
  • Estrategias para comunicar el interés de conceptos matemáticos para estudiantes de ingeniería, Actas del III Simposio i-Test Divulgación de la Ciencia y las Matemáticas, Aranjuez (2012).
  • Carlos Villanueva (ICMAT SO, 2022)
  • Javier Valentín (ICMAT SO, 2021)
  • Javier González Domínguez (ICMAT SO, 2020)
  • David de Hevia (ICMAT JAE, 2020/21)
  • Aitor Mairena Díaz (ICMAT SO, 2019)
  • Eki González García (ICMAT SO, 2019)
  • Pablo Hidalgo Palencia (ICMAT JAE, 2019/20)
  • Antonio Ismael Cano Mármol (ICMAT SO, 2018)
  • José María Gallegos Saliner (ICMAT SO, 2018)
  • Héctor Jardón Sánchez (ICMAT SO, 2017)
  • Pablo Hidalgo Palencia (Universidad Complutense de Madrid, 2019/20): Retículos de Banach libres.
  • Aitor Mairena Díaz (Universidad de Santiago de Compostela, 2019/20): El Teorema de Lomonosov.
  • Héctor Jardón Sánchez (Universidad de Oviedo, 2018/19): Operadores positivos y el problema del subespacio invariante.
  • Carlos Domingo Salazar (Universidad de Barcelona, 2010/11): El problema del subespacio invariante.
  • Jesús Illescas Fiorito (Universidad Complutense de Madrid, 2023/24).
  • Fernando Benito Fernández de la Cigoña (Universidad Autónoma de Madrid, 2023/24).
  • Jorge Santiago Ibáñez Marcos (Universidad Complutense de Madrid, 2022/23): Functional structure of valuation spaces.
  • David Muñoz Lahoz (Universidad Autónoma de Madrid, 2022/23): Band projections on the space of regular operators over a Banach lattice.
  • Enrique García Sánchez (Universidad Complutense de Madrid, 2021/22): El retículo de Banach libre generado por un espacio de Banach.
  • David de Hevia (Universidad Complutense de Madrid, 2020/21): Proyecciones en retículos de Banach.
  • Rafaela Gesing (Universidade de São Paulo, 2018/19, external advisor): Minimal Functions in Banach lattices.
  • David Ruiz Baños (Universidad de Barcelona, 2010/11): Invariant subspaces for isomorphisms on Banach spaces.
  • David de Hevia (Universidad Complutense de Madrid, 2021-)
  • Asma Ben Rjeb (Université de Tunis, 2022-)
  • Enrique García Sánchez (Universidad Complutense de Madrid, 2022-)
  • Jorge Santiago Ibáñez Marcos (Universidad Complutense de Madrid, 2023-)
  • David Muñoz Lahoz (Universidad Autónoma de Madrid, 2023-)
  • University of Cambridge, September-December 2023.
  • LMS visits to the UK (Cambridge, Oxford, Lancaster, Belfast), May 2019.
  • Universidad de Buenos Aires (Argentina), August 2016.
  • Queen's University Belfast (UK), May 2016, February 2018.
  • Newcastle University (UK), June 2015.
  • University of Illinois at Urbana-Champaign (USA), May 2014.
  • Universidad Nacional Autónoma de México (Mexico), August-September 2013.
  • Adam Mickiewiecz University (Poland), June-July 2012.
  • Université Paris VI / CNRS (France), September-December 2007, August-December 2008, April 2016.
  • University of Alberta (Canada), December 2006.
  • University of Missouri-Columbia (USA), September-December 2006.
  • Beca Leonardo (Fundación BBVA), 2022.
  • Premio Extraordinario de Doctorado (Best PhD Thesis in Mathematics). Universidad Complutense de Madrid, 2012.
  • Juan de la Cierva Research position. Ministerio de Ciencia e Innovación, 2009.

Research groups

I am a member of the following research groups in Mathematics



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Universidad Complutense de Madrid

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Universidad de Murcia

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Professional associations

I belong to the following associations and networks.

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Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)

Nicolás Cabrera, no. 13-15 Campus de Cantoblanco, UAM

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