Research

My lines of research embrace Operator Theory, Complex Analysis and Spaces of Analytic Functions. 

I am interested in the Invariant Subspace Problem and in its interactions with Local Spectral Theory and Functional Calculi, specially for compact perturbations of normal operators acting on Hilbert spaces, and with order structures and positivity in Banach lattices.

 I also enjoy studying the interplay between Complex Analysis and Operator Theory in Spaces of Analytic Functions. In this respect, I am mostly interested in composition and weighted composition operators, as well as in Toeplitz and truncated Toeplitz operators.

Articles

• On commutants of composition operators embedded in C0-semigroups
  F. Javier González-Doña
  On preparation (2024)

• Local spectral theory for subordinated operators: the Cesàro operator and Beyond
  Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
  Preprint (2024)

• Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability
  Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
  Preprint (2024)

• Universality arising from invertible weighted composition operators
  Luciano Abadías, F. Javier González-Doña, Jesús Oliva-Maza
  Preprint (2023)

• Rank-one perturbations of cyclic normal operators: Cauchy transforms and functional models
  Eva A. Gallardo-Gutiérrez, F. Javier González-Doña
  Preprint (2023)

• 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 (2024), to appear [arXiv]

• 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
  Linear Algebra and its Applications,  674 (2023), 155–191.

• 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, accepted (2023), to appear [arXiv].

• 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.

Other publications

• 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)

Conference and seminar talks

• 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.