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Banach Space Theory pp 237–289Cite as

Structure of Banach Spaces

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Abstract

The focus of the study in the present chapter is on Banach spaces containing subspaces isomorphic to c 0 or ℓ 1. We prove Sobczyk’s theorem on complementability of c 0 in separable overspaces, lifting property of ℓ 1 and Pełczyński’s characterization of separable Banach spaces containing ℓ 1. We present Rosenthal’s ℓ 1 theorem, Odell–Rosenthal theorem and the Rosenthal–Bourgain–Fremlin–Talagrand theory of Baire-1 functions on Polish spaces.

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Authors and Affiliations

  1. Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, Praha 1, 11567, Prague, Czech Republic

    Marián Fabian & Petr Hájek

  2. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16627, Prague, Czech Republic

    Petr Habala

  3. Departamento de Matematica Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

    Vicente Montesinos

  4. Department of Mathematical and Statistical Sciences, University of Alberta, Central Academic Building, Edmonton, T6G 2G1, Alberta, Canada

    Václav Zizler

Authors
  1. Marián Fabian
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  5. Václav Zizler
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Correspondence to Marián Fabian .

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Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V. (2011). Structure of Banach Spaces. In: Banach Space Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7515-7_5

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