Pedro Tradacete

Learn More

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.

0+

Papers

0+

Citations

0+

Co-authors

0+

Cups of Coffee

Recent and forthcoming

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

Recent advances in Banach lattices

7-12 May 2023

Banff, Canada.

Conference website

Geometric Valuation Theory

5-9 June 2023

CIEM, Castro-Urdiales

Conference website

ICMAT-IMAG Doc-course in Functional Analysis

12-30 June 2023

IMAG-ICMAT, Granada-Madrid.

Conference website

Research term Lattice Structures in Analysis and Applications

1 April - 15 June 2024

ICMAT

Conference website

CIMPA School: Ordered Structures with Applications in Finance and Machine Learning

16-28 June 2024

Université de Carthage, Tunis.

Conference website

Positivity and Banach spaces

1-5 July 2024

Chern Institute of Mathematics, Tianjin, P. R. China.

Conference website

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.
preprint pdf
Y. Azouzi, A. Ben Rjeb, P. Tradacete: The strong Nakano property in Banach lattices.
preprint pdf
D. de Hevia, G. Martínez-Cervantes, A. Salguero-Alarcón, P. Tradacete: A counterexample to the complemented subspace problem in Banach lattices.
preprint pdf
D. Muñoz-Lahoz, P. Tradacete: Band projections in spaces of regular operators. Trans. Amer. Math. Soc (to appear)
preprint pdf
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)
preprint pdf
T. Oikhberg, M.A. Taylor, P. Tradacete, V.G. Troitsky: Free Banach lattices. J. Eur. Math. Soc. (JEMS) (to appear)
preprint pdf
E. Durand-Cartagena, J. Soria, P. Tradacete: The least doubling constant of a path graph. Kyoto J. Math. (to appear)
preprint pdf
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
preprint pdf -- journal website
E. García-Sánchez, P. Tradacete: Free dual spaces and free Banach lattices. J. Math. Anal. Appl. 532 (2024), no. 2, Paper No. 127931.
preprint pdf -- journal website
E. Durand-Cartagena, J. Soria, P. Tradacete: Doubling constants and spectral theory on graphs. Discrete Math. 346 (2023), no. 6, Paper No. 113354.
preprint pdf -- journal website
D. de Hevia, P. Tradacete: Free complex Banach lattices. J. Funct. Anal. 284 (2023), no. 10, Paper No. 109888.
preprint pdf -- journal website
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.
preprint pdf -- journal website
A. Avilés, P. Tradacete: Amalgamation and injectivity in Banach lattices. Int. Math. Res. Not. IMRN 2023, no. 2, 956-997.
preprint pdf -- journal website
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.
preprint pdf -- journal website
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.
preprint pdf -- journal website
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.
preprint pdf -- journal website
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.
preprint pdf -- journal website
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.
preprint pdf -- journal website
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.
preprint pdf -- journal website (OA)
A. Rueda Zoca, P. Tradacete, I. Villanueva: Daugavet property in tensor product spaces. J. Inst. Math. Jussieu 20 (2021), no. 4, 1409-1428.
preprint pdf -- journal website
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.
preprint pdf -- journal website
M. Mathieu, P. Tradacete: Strictly singular multiplication operators on L(X). Israel J. Math. 236 (2020), 685-709.
preprint pdf -- journal website
A. Colesanti, D. Pagnini, P. Tradacete, I. Villanueva: A class of invariant valuations on Lip(Sn-1). Adv. Math. 366 (2020), 107069.
preprint pdf-- journal website
E. A. Sánchez-Pérez, P. Tradacete: p-regularity and weights for operators between Lp spaces. Z. Anal. Anwend. 39 (2020), no. 1, 41-65.
preprint pdf -- journal website
P. Tradacete, I. Villanueva: Valuations on Banach lattices. Int. Math. Res. Not. IMRN 2020, no. 1, 287-319.
preprint pdf -- journal website
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.
preprint pdf -- journal website
J. Soria, P. Tradacete: The least doubling constant of a metric measure space. Ann. Acad. Sci. Fenn. Math. 44 (2019), 1015-1030.
preprint pdf -- journal website
A. Avilés, P. Tradacete, I. Villanueva: The free Banach lattices generated by lp and c0. Rev. Mat. Complutense 32 (2019), no. 2, 353-364.
preprint pdf -- journal website
E. A. Sánchez-Pérez, P. Tradacete: (p,q)-regular operators between Banach lattices. Monatsh. Math. 188 (2019), no. 2, 321-350.
preprint pdf -- journal website
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.
preprint pdf-- journal website
J. Flores, F. L. Hernández, P. Tradacete: Strict singularity: a lattice approach. Positivity and Noncommutative Analysis, Trends Math., Birkäuser (2019), 153--165.
preprint pdf -- journal website
A. Avilés, J. Rodríguez, P. Tradacete: The free Banach lattice generated by a Banach space. J. Funct. Anal. 274 (2018), no. 10, 2955-2977.
preprint pdf -- journal website
Y. Raynaud, P. Tradacete: Calderón-Lozanovskii interpolation on quasi-Banach lattices. Banach J. Math. Anal. 12 (2018), no. 2, 294-313.
preprint pdf -- journal website
P. Tradacete, I. Villanueva: Continuity and representation of valuations on star bodies. Adv. Math. 329 (2018), 361-391.
preprint pdf -- journal website
F. L. Hernández, E. M. Semenov, P. Tradacete: Interpolation and extrapolation of strictly singular operators between Lp spaces. Adv. Math. 316 (2017), 667-690.
preprint pdf -- journal website
J. López-Abad, P. Tradacete: Shellable weakly compact subsets of C[0,1]. Math. Ann. 367 (2017), no. 3-4, 1777-1790.
preprint pdf -- journal website
T. Oikhberg, P. Tradacete: Almost band preservers. Positivity 21 (2017), no. 4, 1393-1423.
preprint pdf -- journal website
T. Oikhberg, P. Tradacete: Almost disjointness preservers. Canad. J. Math. 69 (2017), no. 3, 650-686.
preprint pdf -- journal website
P. Tradacete, I. Villanueva: Radial continuous valuations on star bodies. J. Math. Anal. Appl. 454 (2017), no. 2, 995-1018.
preprint pdf -- journal website
A. Avilés, A. J. Guirao, S. Lajara, J. Rodríguez, P. Tradacete: Weakly compactly generated Banach lattices. Studia Math. 234 (2016), 165-183.
preprint pdf -- journal website
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).
preprint pdf -- journal website
J. Flores, J. López-Abad, P. Tradacete: Banach lattice versions of strict singularity. J. Funct. Anal. 270 (2016), 2715-2731.
preprint pdf -- journal website
J. López-Abad, P. Tradacete: Bases of random unconditional convergence in Banach spaces. Trans. Amer. Math. Soc. 368 (2016), 9001-9032.
preprint pdf -- journal website
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.
journal website
E. M. Semenov, P. Tradacete, F. L. Hernández: Strictly singular operators on pairs of Lp spaces. Dokl. Math. 94 (2016), 450-452.
journal website
J. Soria, P. Tradacete: Best constants for the Hardy-Littlewood maximal operator on finite graphs. J. Math. Anal. Appl. 436 (2016), 661-682.
preprint pdf -- journal website
J. Soria, P. Tradacete: Optimal rearrangement invariant range for Hardy type operators. Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), no. 4, 865-893.
preprint pdf -- journal website
J. Soria, P. Tradacete: Characterization of the restricted type spaces R(X). Math. Inequal. Appl. 18 (2015), 295-319.
preprint pdf -- journal website
P. Tradacete: Positive Schur properties in spaces of regular operators. Positivity 19 (2015), no 2, 305-316.
preprint pdf -- journal website
F. L. Hernández, E. M. Semenov, P. Tradacete: Rearrangement invariant spaces with Kato property. Funct. Approx. Comment. Math. 50 (2014), no 2, 215-232.
preprint pdf -- journal website
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.
preprint pdf -- journal website
J. López-Abad, C. Ruiz, P. Tradacete: The convex hull of a Banach-Saks set. J. Funct. Anal. 266 (2014), 2251-2280.
preprint pdf -- journal website
E. A. Sánchez-Pérez, P. Tradacete: Positively norming sets in Banach function spaces. Q. J. Math. 65 (2014), 1049-1068.
preprint pdf -- journal website
M. J. Carro, P. Tradacete: Extrapolation on Lp,∞(μ). J. Funct. Anal. 265 (2013), 1840-1869.
preprint pdf -- journal website
P. Tradacete: Spectral properties of disjointly strictly singular operators, J. Math. Anal. Appl. 395 (2012), 376-384.
preprint pdf -- journal website
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.
preprint pdf -- journal website
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.
preprint pdf -- journal website
J. Flores, F. L. Hernández, P. Tradacete: Domination problems for strictly singular operators and other related classes, Positivity 15 (2011), 595-616.
preprint pdf -- journal website
P. Tradacete: c0-singular and l1-singular operators between vector-valued Banach lattices, Positivity 15 (2011), 241-251.
preprint pdf -- journal website
P. Tradacete: Subspace structure of Lorentz Lpq spaces and strictly singular operators, J. Math. Anal. Appl. 367 (2010), 98-107.
preprint pdf -- journal website
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.
preprint pdf -- journal website
F.L. Hernández, E. M. Semenov, P. Tradacete: Strictly singular operators on Lp spaces and interpolation, Proc. Amer. Math. Soc. 138 (2010), 675-686.
preprint pdf -- journal website
J. Flores, P. Tradacete, V.G. Troitsky: Disjointly homogeneous Banach lattices and compact products of operators, J. Math. Anal. Appl. 354 (2009), 657-663.
preprint pdf -- journal website
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.
preprint pdf -- journal website
J. Flores, P. Tradacete: Factorization and domination of positive Banach-Saks operators, Studia Math. 189 (2008), 91-101.
preprint pdf -- journal website
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.
preprint pdf -- journal website
J. Flores, F.L. Hernández, P. Tradacete: Powers of operators dominated by strictly singular operators, Q. J. Math. 59 (2008), 321-334.
preprint pdf -- journal website

VITA

  • 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.
COURSES
  • 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)
PUBLICATIONS
  • 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).
INTRODUCTION TO RESEARCH
  • 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)
UNDERGRADUATE
  • 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.
MASTER
  • 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.
PHD
  • 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

MATHEMATICAL ANALYSIS AND DIFFERENTIAL EQUATIONS

ICMAT

Read More

OPERATORS, LATTICES AND BANACH SPACES

Universidad Complutense de Madrid

Read More

TOPOLOGY, ANALYSIS AND SETS

Universidad de Murcia

Read More

Professional associations

I belong to the following associations and networks.

RSME

Real Sociedad Matemática Española

EMS

European Mathematical Society

NFAAS

Network on Mathematical Analysis and its Applications

Contact Me

pedro.tradacete()icmat.es

Office 407

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

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

28049 Madrid SPAIN