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SeparableG spaces are isomorphic toC(K) spaces

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Abstract

We show that a wide class of separable preduals ofL 1(μ) spaces, namely, theG spaces, introduced by Grothendieck, are isomorphic toC(K) spaces.

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References

  1. Y. Benyamini and J. Lindenstrauss,A predual of l 1 which is not isomorphic to a C(K) space, Israel J. Math.13 (1972), 246–254.

    Article  MathSciNet  Google Scholar 

  2. H. Fakhouri,Projections contractantes dans C(X), Seminaire Choquet (Initiation a l’analyse) 10e année, 1970/71, communication no. 5.

  3. A. Grothendieck,Une caractérisation vectorielle métrique des espaces L 1, Canad. J. Math.7 (1955), 552–561.

    MATH  MathSciNet  Google Scholar 

  4. S. Kakutani,Concrete representation of abstract M spaces, Ann. Math.42 (1941), 994–1024.

    Article  MathSciNet  Google Scholar 

  5. A. Lazar and J. Lindenstrauss,Banach spaces whose duals are L 1 spaces and their reresenting matrices, Acta Math.126 (1971), 165–193.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Lindenstrauss,Extension of compact operators, Mem. Amer. Math. Soc. No. 48, 1964.

  7. J. Lindenstrauss and D. E. Wulbert,On the classification of the banach spaces whose duals are L 1 spaces, J. Functional Analysis4, (1969), 332–349.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Mazurkiewic and W. Sierpinski,Contribution à la topologie des ensembles dénombrables, Fund. Math.1 (1920), 17–27.

    Google Scholar 

  9. A. Milutin,Isomorphism of spaces of continuous functions on compacts of power continuum, Teor. Funkcii Funkcional. Anal. i Prilozen2 (1966), 150–156 (Russian).

    Google Scholar 

  10. A. Peŀczyński,On C(S) subspaces of separable Banach spaces, Studia Math.31 (1968), 513–522.

    MathSciNet  Google Scholar 

  11. C. Samuel,Sur certains espaces C σ(S) et sur les sous-espaces complémentés de C(S), Bull. Sci. Math. 2e série95 (1971), 65–82.

    MATH  MathSciNet  Google Scholar 

  12. Z. Semadeni,Spaces of continuous functions, Warsaw, 1971.

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Authors and Affiliations

  1. The Hebrew University of Jerusalem, Jerusalem, Israel

    Y. Benyamini

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  1. Y. Benyamini
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Additional information

This is a part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss. I wish to thank Professor Lindenstrauss for his interest and advice.

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Benyamini, Y. SeparableG spaces are isomorphic toC(K) spaces. Israel J. Math. 14, 287–293 (1973). https://doi.org/10.1007/BF02764890

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  • DOI: https://doi.org/10.1007/BF02764890

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