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Jorge López

Institution: Consejo Superior de Investigaciones Científicas

Position: Ramón y Cajal.

               Maître de Conférences Université Paris 7 (détachement).

Office: 301        Phone:+34 912999 761

E-mail: abad()icmat.es

Personal Webpage

 

Biographical Review

My fields of research are combinatorics, functional analysis and set theory. I work in applications of Ramsey theory and infinite combinatorics to the study of the geometry of Banach spaces, producing new examples of spaces and also giving structural results. More concretely, I am interested in several weak notions of unconditionality for a basic sequence, in the role of compact families of finite sets in Banach spaces, or in the Banach-Saks property of a set.

Recently, I have been working in the existence of unconditional basic sequences in a Banach space. We have partially solved the separable quotient problem for spaces of large density.

I have coauthored more than 20 papers, including articles in Advances in Mathematics, Mathematische Annalen and Journal of Functional Analysis.

Research Interest

 

  • Ramsey Theory:
    • Structural Ramsey Theory.
    • Applications.
  • Geometry of Banach spaces:
    • Unconditional basic sequences.
    • Few operators.
    • Separable Quotient Problem.
    • Generic Banach spaces. 
  • Combinatorial Set Theory and its applications

 

Publications

  •  ï»¿J. Bagaria & J. Lopez-Abad, Weakly Ramsey sets in Banach spaces, Advances in  Mathematics 160 (2001), no. 2, 133-174.
  •  J. Bagaria & J. Lopez-Abad, Determinacy and weakly Ramsey sets in Banach spaces.  Transactions of the American  Mathematical Society 354 (2002), no. 4, 1327-1349.
  •  J. Lopez Abad,  Canonical equivalence relations on FINk. Tagungsberich Oberwolfach. (2002).
  •  S. A. Argyros, J. Lopez-Abad & S. Todorcevic,   A class of Banach spaces with no  unconditional basic sequence. C. R. Acad. Sci. Paris, Ser. I  337 (2003) 43-48.
  • S. A. Argyros, J. Lopez-Abad & S. Todorcevic, A class of Banach spaces with few non strictly singular operators.  Journal of Functional Analysis 222 (2005),  no. 2   306-384.
  •  J. Lopez-Abad, Coding into Ramsey sets.  Mathematische Annalen 332 (2005), no. 4 775-794.
  •  J. Lopez-Abad & S. Todorcevic, Partial unconditionality of weakly null sequences. RACSAM. Special issue on geometry of Banach spaces,  100 (2006)  237-277.
  •  J. Lopez-Abad, Canonical equivalence relations on nets of PSc0. Discrete  Mathematics 307 (2007), no. 23 , 2943-2978.
  •   J. Lopez-Abad &  L. Nguyen Van Thé, The oscillation stability problem for the Urysohn sphere: A combinatorial approach.  Topology and its Applications 155 (2008), no 14, 1516-1530.
  •  P. Dodos & J. Lopez-Abad,  On unconditionally saturated Banach spaces. Studia Mathematica 188 (2008), no 2, 175-191.
  •  J. Lopez-Abad & A. Manoussakis, A classification of Tsirelson type spaces.  Canadian Journal of Mathematics,  60 (2008), No.5, pp. 1108-1148.
  •  J. Lopez-Abad y S. Todorcevic, Pre-compact families of finite sets  of integers and weakly null sequences in Banach spaces.  Topology and it Applications, 156 (2009),  pp. 1396-1411.
  •  J. Lopez-Abad y S. Todorcevic, A c0-saturated Banach space with no long unconditional basic sequences.  Transactions of the American Society  361 (2009) 4541-4560.
  •  C. A. Di Prisco & J. Lopez-Abad, Teoría de Ramsey y Espacios de Banach. XXI Escuela Venezolana De Matemáticas. Ediciones IVIC. ISBN 978-980-261-101-0 Caracas. 2008.
  •  P. Dodos, J. Lopez-Abad & S. Todorcevic,  Banach spaces and Ramsey Theory: some open problems. RACSAM 104 (2), 2010, 435–450.
  •  P. Dodos, J. Lopez-Abad & S. Todorcevic, Unconditional basic sequences in spaces of high density. Advances in Mathematics 226, (2011), pp. 3297-3308
  •  J. Lopez-Abad y S. Todorcevic,  Generic Banach spaces and generic simplexes. Journal of Functional Analysis 261 (2), (2011), 300--386.
  • P. Dodos, J Lopez-Abad y S. Todorcevic, Partition ideals belows $\aleph_\omega$,  Fund. Math. 217 (2012), no. 1, 21–34.
  • J. Lopez, Some problems concerning basic sequences in Banach spaces, Extracta Math.   26 (2) (2012), 295-316.
  • J. Lopez-Abad y S. Todorcevic, Positional graphs and conditional structure of weakly null sequences.   Advances in Mathematics    242 ,   (2013)  163–186.
  • J. Lopez-Abad, A Bourgain-Pisier construction for general Banach spaces.    Journal of Functional Analysis   265  (2013), no 7,   1423-1441.
  • J. Lopez-Abad, Large cardinals and basic sequences. To appear in  Annals of Pure and Applied Logic. DOI 10.1016/j.apal.2013.06.016
     
  • J. Lopez-Abad,  C. Ruiz  y P. Tradacete.  The convex hull of a Banach-Saks set. To appear in  Journal of Functional Analysis. DOI 10.1016/j.jfa.2013.06.020