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Asymptotic Infinite-Dimensional Theory of Banach Spaces

  • Bernard Maurey
  • Vitali Milman
  • Nicole Tomczak-Jaegermann
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

In this paper we study structural properties of infinite dimensional Banach spaces. The classical understanding of such properties was developed in the 50s and 60s; goals of the theory had direct roots in and were natural expansion of problems from the times of Banach. Most of surveys and books of that period directly or indirectly discussed such problems as the existence of unconditional basic sequences, the c0- 1-reflexive subspace problem and others. However, it has been realized recently that such a nice and elegant structural theory does not exist. Recent examples (or counter-examples to classical problems) due to Gowers and Maurey [GM] and Gowers [G.2], [G.3] showed much more diversity in the structure of infinite dimensional subspaces of Banach spaces than was expected.

Keywords

Banach Space Natural Basis Winning Strategy Spreading Model Unconditional Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Bernard Maurey
    • 1
  • Vitali Milman
    • 2
    • 3
  • Nicole Tomczak-Jaegermann
    • 4
  1. 1.Equipe d’Analyse et Math. Appl.Université de Marne la ValléeNoisy Le Grand CEDEXFrance
  2. 2.School of Math. Sci. Sackler Fac. of Exact Sci.Tel Aviv UniversityTel AvivIsrael
  3. 3.Dept. of Math.Ohio State UniversityColumbusUSA
  4. 4.Department of MathematicsUniversity of AlbertaEdmontonCanada

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