Research

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RESEARCH INTERESTS

My research focuses mainly on functional analysis, with a particular emphasis on Banach spaces and Banach lattices, although connections to other areas of mathematics are frequent. My main lines of work include:

• Spaces of continuous functions in compact spaces (C(K) spaces), and its interactions with set theory, topology and combinatorics.
• Categorical and homotopical methods applied to Banach spaces and Banach lattices.
• Complex interpolation with application to Fourier multipliers.

Some keywords are: almost disjoint families, polyhedral spaces, complemented subspaces, twisted sums, exact sequences, lifting and extension of operators, free Banach lattices, analytic families, unimodular multipliers.

PREPRINTS AND PAPERS

1. New results on Fourier multipliers on L^p: a perspective through unimodular symbols (with M. J. Carro), preprint. arXiv
2. Free quasi-Banach lattices (with P. Tradacete and N. Trejo-Arroyo), preprint. arXiv
3. Derived functors associated to the ideal of compact operators in Banach spaces (with F. Cabello Sánchez, J. M. F. Castillo and N. Trejo-Arroyo), preprint. arXiv
4. A negative solution for the complemented subspace problem in Banach lattices (with D. de Hevia, G. Martínez-Cervantes and P. Tradacete), to appear in J. Eur. Math. Soc.  arXiv
5. Polyhedrality for twisted sums with C(ω^α) (with J. M. F. Castillo), Studia Math. 284, No. 1, 91-99 (2025).  arXiv | journal
6. The complemented subspace for C(K)-spaces: A counterexample (with G. Plebanek), Adv. Math. 426. Paper No. 109103, 20 p. (2023).  arXiv | journal
7. When Kalton and Peck met Fourier (with F. Cabello Sánchez), Ann. Inst. Fourier (Grenoble) 73, No. 5, 1843-1883 (2023).  arXiv | journal
8. Twisted sums with c₀(I) (with J. M. F. Castillo), Quaest. Math. 46, No. 11, 2339-2554 (2023).  arXiv | journal
9. On the three-space property for C(K)-spaces (with G. Plebanek), J. Funct. Anal. 281, No. 9, Paper No. 109193, 15 p. (2021). arXiv | journal
10. Sailing over three problems of Koszmider (with F. Cabello Sánchez, J. M. F. Castillo, W. Marciszewski and G. Plebanek), J. Funct. Anal. 279, No. 4., Paper No. 108571, 21 p. (2020). arXiv | journal
11. The behavior of quasi-linear maps on C(K)-spaces (with F. Cabello Sánchez and J. M. F. Castillo), J. Math. Anal. Appl. 475, No. 2, 1714-1719 (2019). arXiv | journal

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RECENT, PLANNED AND PROSPECTIVE EVENTS 

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