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C(K) quotients of separable ℒ∞ spaces

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Abstract

It is shown that ifX is an ℒ⫗ space with separable dual, thenX has a quotient isomorphic toC(ω)α if, and only if, there is anɛ >0, such that theɛ-Szlenk index ofX is at leastα. It was previously known, that ifX is a separable ℒ⫗ space with a non-separable dual, thenX has a quotient isomorphic toC[0, 1].

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Iinstitute of Technology, 02139, Cambridge, Mass., USA

    D. E. Alspach & Y. Benyamini

  2. Mathematics Department, Technion—Israel Institute of Technology, Haifa, Israel

    D. E. Alspach & Y. Benyamini

Authors
  1. D. E. Alspach
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  2. Y. Benyamini
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Research partially supported by NSF Grant MCS-74-07509-A03.

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Alspach, D.E., Benyamini, Y. C(K) quotients of separable ℒ∞ spaces. Israel J. Math. 32, 145–160 (1979). https://doi.org/10.1007/BF02764911

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  • DOI: https://doi.org/10.1007/BF02764911

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