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Complex Banach spaces whose duals areL 1-spaces

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Abstract

We prove that for a complex Banach spaceA the following properties are equivalent:

  1. i)

    A * is isometric to anL 1(μ)-space;

  2. ii)

    every family of 4 balls inA with the weak intersection property has a non-empty intersection;

  3. iii)

    every family of 4 balls inA such that any 3 of them have a non-empty intersection, has a non-empty intersection.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Agricultural University of Norway, 1432, AAS-NLH, Norway

    Asvald Lima

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  1. Asvald Lima
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Lima, A. Complex Banach spaces whose duals areL 1-spaces. Israel J. Math. 24, 59–72 (1976). https://doi.org/10.1007/BF02761429

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  • DOI: https://doi.org/10.1007/BF02761429

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