My lines of research embrace Operator Theory, Complex Analysis and Spaces of Analytic Functions.
I focus in studying the structure of operators through their invariant subspaces and their (local) spectral properties. In this sense, I have dealt with compact perturbations of normal operators acting on Hilbert spaces, as well as positive operators on Banach lattices.
I also enjoy studying the interaction between Complex Analysis and Operator Theory considering operators acting on Banach spaces of analytic functions. In this respect, I am mostly interested in composition and weighted composition operators, integration operators and (truncated) Toeplitz operators, and their interaction with the theory of C0-semigroups.
Local spectral theory for subordinated operators: the Cesàro operator and Beyond
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Journal of the London Mathematical Society (2) 112 (2025), no. 2, Paper No. e70273.
On commutants of composition operators embedded in C0-semigroups
F. Javier González-Doña,
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 119, article number 102, (2025).
Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Journal of Functional Analysis, Volume 289, Issue 2, 110903 (2025).
Universality arising from invertible weighted composition operators
Luciano Abadías, F. Javier González-Doña, Jesús Oliva-Maza
Journal of Mathematical Analysis and Applications, Volume 545, Issue 1, 1 May 2025, 129129.
Dunford property (C) for composition operators on H^p spaces
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña, Miguel Monsalve-López
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, accepted for publication (2024), in press [arXiv]
Finite rank perturbations of normal operators: hyperinvariant subspaces and a problem of Pearcy
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Indiana University Mathematics Journal 73 (2024), no. 4, 1551-1578.
Finite rank perturbations of normal operators: spectral idempotents and decomposability
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Journal of Functional Analysis 285 (12), 110148 (2023).
Band-diagonal operators on Banach lattices: matrix dynamics and invariant subspaces
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Linear Algebra and its Applications, 674 (2023), 155–191.
Reducing subspaces for rank-one perturbations of normal operators
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153 (2023), no. 4, 1391–1423.
Invariant subspaces for positive operators on Banach spaces with unconditional basis
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña, Pedro Tradacete
Proceedings of the American Mathematical Society, 150 (2022), no. 12, 5231–5242.
Finite rank perturbations of normal operators: spectral subspaces and Borel series
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Journal de Mathématiques Pures et Appliquées, (9) 162 (2022), 23–75.
On frequencies of parabolic Koenigs domains
Carlos Gómez-Cabello, F. Javier González-Doña [arXiv]
Rank-one perturbations of cyclic normal operators: Cauchy transforms and functional models
Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
Invariant subspaces for classes of operators: finite rank perturbations of normal operators and positive operators
PhD Thesis, Universidad Complutense de Madrid, supervised by Eva A. Gallardo-Gutiérrez (2023)
Approximation and the full Müntz-Szász theorem
Diego Bolón, Clara María Corbalán, F. Javier González-Doña, Daniel Nieves, Carlos C .Oitavén, Alicia Quero, Pedro J. Miana
TEMat monográficos, vol. 1, 33-45 (2020)
Operadores universales y subespacios invariantes
Master Thesis, Universidad de Sevilla, supervised by Miguel Lacruz and Luis Rodríguez-Piazza (2019)
Operadores de composición y clases de Schatten
Degree Thesis, Universidad de Sevilla, supervised by Miguel Lacruz and Luis Rodríguez-Piazza (2018)
Talk at "Iberoamerican Seminar of Mathematical Analysis and Applied Mathematics", July 2025. Title: Some perspectives on the Invariant Subspace Problem.
Talk at "Hilbert Function Spaces", Università degli Studi di Roma Tor Vergata, June 2025. Title: On commutants of composition operators embedded into C_0-semigroups.
Talk at "Q-Math Seminar", Universidad Carlos III de Madrid, March 2025. Title: An insight into commutants, idempotents and structure of operators.
Talk at "Complex Analysis Seminar", Universidad Autónoma de Madrid, March 2025. Title: On commutants of composition operators embedded into C_0-semigroups.
Talk at "IUMA-Day on Analytic and Geometric Methods in Operator Theory", Universidad de Zaragoza, January 2025. Title: Weighted composition operators: universality, commutants and semigroups.
Talk at "VI Encuentro RSME-SMM", Universidad Politécnica de Valencia, July 2024. Title: Dunford property (C) for composition operators on Hp-spaces.
Talk at "Advances Courses on Operator Theory and Complex Analysis", Universidad de La Laguna, June 2024. Title: Dunford property (C) for composition operators on Hp-spaces.
Talk at "IMUS Seminar" in Instituto de Matemáticas de la Universidad de Sevilla (IMUS), June 2024. Title: Local spectral theory for composition operators on Hp-spaces.
Talk at "Workshop Holomorphic Flows vs Semigroup (Operator Theory)" in ICMAT, Madrid, November 2023. Title: Universality arising from invertible weighted composition operators.
Talk at "Bringing Young Mathematicians Together" in ICMAT, Madrid, November 2023. Title: Dunford property (C) for composition operators on Hp-spaces.
Talk at "GAMA Seminar" in Universidad Carlos III de Madrid, October 2023. Title: Invariant subspaces for compact perturbations of normal operators.
Talk at "Advances Courses on Operator Theory and Complex Analysis", University of Thesaloniki, June 2023. Title: Finite rank perturbations of normal operators: invariant subspaces and decomposability.
Talk at "XXI Encuentros de Análisis Real y Complejo", Universidad de Extremadura, May 2023. Title: Invariant subspaces for compact perturbations of normal operators.
Talk at "Mathematical Analysis Seminar", Universidad de Málaga, May 2023, Title: Finite rank perturbations of normal operators: invariant subspaces and decomposability.
Talk at "Rubio de Francia Seminar", Universidad de Zaragoza, March 2023. Title: Finite rank perturbations of normal operators: invariant subspaces and decomposability.
Talk at "VI Meeting of Young Researchers of RSME", Universidad de León, Febrero 2023. Title: Finite rank perturbations of normal operators: invariant subspaces and decomposability.
Talk at "Bringing Young Mathematicians Together", Universidad de Valencia (online), December 2022. Title: Local spectral theory and invariant subspaces.
Talk at "Young Researchers in Functional Analysis and Mathematical Physics'22", Universidade do Algarve, June 2022. Title: Invariant subspaces for finite rank perturbations of normal operators.
Talk at "Workshop on Banach spaces and Banach lattices II", ICMAT, Madrid, May 2022. TItle: Invariant subspaces for positive operators on Banach lattices with unconditional basis.
Talk at "PhD Seminar", Universidad Complutense de Madrid, April 2022. Title: How to dissect a spectrum: from normal operators to decomposable operators.
Talk at "Bienal RSME, special session of Functional Analysis", Universidad de Castilla-La Mancha, January 2022. Title: Invariant subspaces for positive operators.
Talk at "Frontiers of Operator Theory", CIRM, Luminy, December 2021. Title: Invariant subspaces for finite rank perturbations of diagonal operators.
Talk at "Complex Analysis Lab Seminar", Università di Bologna, November 2021. Title: Halmos' invariant subspace problem and local spectral theory.
Talk at "Complex Analysis Lab Seminar", Università di Bologna, October 2021. Title: A brief introduction to Invariant Subpsace Problem.
Talk at "II Workshop of Functional Analysis and Applications Spanish Network" online, September 2021. Title: Invariant subspaces for rank-one perturbations of diagonal operators.
Talk at "Trend in Operator Theory and its applications", Universidade de Lisboa, June 2021. Title: Reducing subspaces for rank-one perturbations of diagonal operators.
Talk at "PhD Seminar", Universidad Complutense de Madrid, June 2021. TItle: Invariant subspaces for compact perturbations of normal operators.
Talk at "Bringing Young Mathematicians Together", Universidad de Valencia (online), December 2020. Title: Invariant subspaces for positive operators on Banach lattices with unconditional basis.
Talk at "XV Encuentros de Investigación en Teoría de la Aproximación", Universidad de Zaragoza (online), November 2020. TItle: Invariant subspaces for positive operators on Banach lattices with unconditional basis.
Talk at "Rubio de Francia Seminar", Universidad de Zaragoza (online), November 2020. Title: Reducing subspaces for rank-one perturbations of diagonal operators.