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. In 2011, I came back to Madrid where I lectured as Profesor Ayudante Doctor at Universidad Carlos III de Madrid until 2018, when I became full-time researcher 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.

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Papers

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Citations

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Co-authors

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Cups of Coffee

Recent and forthcoming

Postdoc position at ICMAT

AEI-DFG project "Operator Theory on Free Banach lattices"

Instructions for application: website

Deadline: 15 December 2024

Structures in Banach Spaces

17-21 March 2025

Erwin Schrödinger Institute, Vienna, Austria.

Conference website

Phase retrieval & Banach lattices

5-9 May 2025

ETH Zürich, Switzerland.

Conference website

Functional and Metric Analysis and their Interactions

25-30 May 2025

BIRS-IMAG, Granada.

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. Bilokopytov, E. García-Sánchez, D. de Hevia, G. Martínez-Cervantes, P. Tradacete: Norm-attaining lattice homomorphisms and renormings of Banach lattices.
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A. Avilés, C. Rosendal, M. A. Taylor, P. Tradacete: Coordinate systems in Banach spaces and lattices.
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W. Corrêa, V. Ferenczi, R. Gesing, P. Tradacete: Extremes of interpolation scales of Banach spaces.
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N. J. Laustsen, P. Tradacete: Banach lattices of positively homogeneous functions induced by a Banach space.
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Y. Azouzi, A. Ben Rjeb, P. Tradacete: The strong Nakano property in Banach lattices.
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D. de Hevia, G. Martínez-Cervantes, A. Salguero-Alarcón, P. Tradacete: A counterexample to the complemented subspace problem in Banach lattices.
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D. Muñoz-Lahoz, P. Tradacete: Banach lattice AM-algebras. Proc. Amer. Math. Soc. (to appear)
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T. Oikhberg, M.A. Taylor, P. Tradacete, V.G. Troitsky: Free Banach lattices. J. Eur. Math. Soc. (JEMS) (to appear)
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E. García-Sánchez, D. H. Leung, M. A. Taylor, P. Tradacete: Banach lattices with upper p-estimates: free and injective objects. Math. Ann. 391 (2025), 3363-3398.
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E. Durand-Cartagena, J. Soria, P. Tradacete: The least doubling constant of a path graph. Kyoto J. Math. 65 (2025), no. 1, 217-243.
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D. Muñoz-Lahoz, P. Tradacete: Band projections in spaces of regular operators. Trans. Amer. Math. Soc 377 (2024), No. 7, 5197-5218.
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E. García-Sánchez, D. de Hevia, P. Tradacete: Free objects in Banach space theory. In Cutting-Edge Mathematics. RSME 2022. RSME Springer Series, vol 13 (2024).
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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
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E. García-Sánchez, P. Tradacete: Free dual spaces and free Banach lattices. J. Math. Anal. Appl. 532 (2024), no. 2, Paper No. 127931.
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E. Durand-Cartagena, J. Soria, P. Tradacete: Doubling constants and spectral theory on graphs. Discrete Math. 346 (2023), no. 6, Paper No. 113354.
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D. de Hevia, P. Tradacete: Free complex Banach lattices. J. Funct. Anal. 284 (2023), no. 10, Paper No. 109888.
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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.
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A. Avilés, P. Tradacete: Amalgamation and injectivity in Banach lattices. Int. Math. Res. Not. IMRN 2023, no. 2, 956-997.
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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.
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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.
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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.
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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.
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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.
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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.
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A. Rueda Zoca, P. Tradacete, I. Villanueva: Daugavet property in tensor product spaces. J. Inst. Math. Jussieu 20 (2021), no. 4, 1409-1428.
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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.
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M. Mathieu, P. Tradacete: Strictly singular multiplication operators on L(X). Israel J. Math. 236 (2020), 685-709.
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A. Colesanti, D. Pagnini, P. Tradacete, I. Villanueva: A class of invariant valuations on Lip(Sn-1). Adv. Math. 366 (2020), 107069.
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E. A. Sánchez-Pérez, P. Tradacete: p-regularity and weights for operators between Lp spaces. Z. Anal. Anwend. 39 (2020), no. 1, 41-65.
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P. Tradacete, I. Villanueva: Valuations on Banach lattices. Int. Math. Res. Not. IMRN 2020, no. 1, 287-319.
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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.
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J. Soria, P. Tradacete: The least doubling constant of a metric measure space. Ann. Acad. Sci. Fenn. Math. 44 (2019), 1015-1030.
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A. Avilés, P. Tradacete, I. Villanueva: The free Banach lattices generated by lp and c0. Rev. Mat. Complutense 32 (2019), no. 2, 353-364.
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E. A. Sánchez-Pérez, P. Tradacete: (p,q)-regular operators between Banach lattices. Monatsh. Math. 188 (2019), no. 2, 321-350.
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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.
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J. Flores, F. L. Hernández, P. Tradacete: Strict singularity: a lattice approach. Positivity and Noncommutative Analysis, Trends Math., Birkäuser (2019), 153--165.
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A. Avilés, J. Rodríguez, P. Tradacete: The free Banach lattice generated by a Banach space. J. Funct. Anal. 274 (2018), no. 10, 2955-2977.
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Y. Raynaud, P. Tradacete: Calderón-Lozanovskii interpolation on quasi-Banach lattices. Banach J. Math. Anal. 12 (2018), no. 2, 294-313.
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P. Tradacete, I. Villanueva: Continuity and representation of valuations on star bodies. Adv. Math. 329 (2018), 361-391.
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F. L. Hernández, E. M. Semenov, P. Tradacete: Interpolation and extrapolation of strictly singular operators between Lp spaces. Adv. Math. 316 (2017), 667-690.
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J. López-Abad, P. Tradacete: Shellable weakly compact subsets of C[0,1]. Math. Ann. 367 (2017), no. 3-4, 1777-1790.
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T. Oikhberg, P. Tradacete: Almost band preservers. Positivity 21 (2017), no. 4, 1393-1423.
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T. Oikhberg, P. Tradacete: Almost disjointness preservers. Canad. J. Math. 69 (2017), no. 3, 650-686.
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P. Tradacete, I. Villanueva: Radial continuous valuations on star bodies. J. Math. Anal. Appl. 454 (2017), no. 2, 995-1018.
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A. Avilés, A. J. Guirao, S. Lajara, J. Rodríguez, P. Tradacete: Weakly compactly generated Banach lattices. Studia Math. 234 (2016), 165-183.
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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).
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J. Flores, J. López-Abad, P. Tradacete: Banach lattice versions of strict singularity. J. Funct. Anal. 270 (2016), 2715-2731.
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J. López-Abad, P. Tradacete: Bases of random unconditional convergence in Banach spaces. Trans. Amer. Math. Soc. 368 (2016), 9001-9032.
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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.
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E. M. Semenov, P. Tradacete, F. L. Hernández: Strictly singular operators on pairs of Lp spaces. Dokl. Math. 94 (2016), 450-452.
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J. Soria, P. Tradacete: Best constants for the Hardy-Littlewood maximal operator on finite graphs. J. Math. Anal. Appl. 436 (2016), 661-682.
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J. Soria, P. Tradacete: Optimal rearrangement invariant range for Hardy type operators. Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), no. 4, 865-893.
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J. Soria, P. Tradacete: Characterization of the restricted type spaces R(X). Math. Inequal. Appl. 18 (2015), 295-319.
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P. Tradacete: Positive Schur properties in spaces of regular operators. Positivity 19 (2015), no 2, 305-316.
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F. L. Hernández, E. M. Semenov, P. Tradacete: Rearrangement invariant spaces with Kato property. Funct. Approx. Comment. Math. 50 (2014), no 2, 215-232.
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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.
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J. López-Abad, C. Ruiz, P. Tradacete: The convex hull of a Banach-Saks set. J. Funct. Anal. 266 (2014), 2251-2280.
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E. A. Sánchez-Pérez, P. Tradacete: Positively norming sets in Banach function spaces. Q. J. Math. 65 (2014), 1049-1068.
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M. J. Carro, P. Tradacete: Extrapolation on Lp,∞(μ). J. Funct. Anal. 265 (2013), 1840-1869.
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P. Tradacete: Spectral properties of disjointly strictly singular operators, J. Math. Anal. Appl. 395 (2012), 376-384.
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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.
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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.
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J. Flores, F. L. Hernández, P. Tradacete: Domination problems for strictly singular operators and other related classes, Positivity 15 (2011), 595-616.
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P. Tradacete: c0-singular and l1-singular operators between vector-valued Banach lattices, Positivity 15 (2011), 241-251.
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P. Tradacete: Subspace structure of Lorentz Lpq spaces and strictly singular operators, J. Math. Anal. Appl. 367 (2010), 98-107.
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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.
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F.L. Hernández, E. M. Semenov, P. Tradacete: Strictly singular operators on Lp spaces and interpolation, Proc. Amer. Math. Soc. 138 (2010), 675-686.
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J. Flores, P. Tradacete, V.G. Troitsky: Disjointly homogeneous Banach lattices and compact products of operators, J. Math. Anal. Appl. 354 (2009), 657-663.
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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.
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J. Flores, P. Tradacete: Factorization and domination of positive Banach-Saks operators, Studia Math. 189 (2008), 91-101.
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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.
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J. Flores, F.L. Hernández, P. Tradacete: Powers of operators dominated by strictly singular operators, Q. J. Math. 59 (2008), 321-334.
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VITA

  • Free Banach lattices generated by finite dimensional spaces. Positivity and Banach spaces, Chern Institute of Mathematics, Nankai University, China. July 2024.
  • 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.
  • Phase retrieval & Banach lattices, ETH Zürich, 5-9 May 2025. website
  • 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
  • Raúl Enrique Pariente (ICMAT SO, 2024)
  • 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
  • Gonzalo Martínez Fernández (Universidad Complutense de Madrid, 2024/25).
  • Jesús Illescas Fiorito (Universidad Complutense de Madrid, 2023/24): Phase retrieval and stable phase retrieval in Banach lattices.
  • Fernando Benito Fernández de la Cigoña (Universidad Autónoma de Madrid, 2023/24): Minimizadores doblantes.
  • 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-)
  • Nazaret Trejo Arroyo (Universidad Complutense de Madrid, 2024-)
  • Jesús Illescas Fiorito (Universidad Complutense de Madrid, 2024-)
  • Nankai University (China), July 2024.
  • 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

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OPERATORS, LATTICES AND BANACH SPACES

Universidad Complutense de Madrid

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TOPOLOGY, ANALYSIS AND SETS

Universidad de Murcia

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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