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An extension theorem for separable Banach spaces

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Abstract

We construct a totally disconnected ω*, norming subsetF of the unit ballB * of an arbitrary separable Banach space,X, and an operator fromC(F) toC(B*) that “amost” commutes with the natural embeddings ofX. This is used to give a new proof of Milutin's theorem and to prove some new results on complemented subspaces ofC[0, 1] with separable dual. In particular we show that a complemented subspace ofC(ωω), is either isomorphic toC(ωω) or toc u.

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, 43210, Columbus, Ohio, USA

    Y. Benyamini

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  1. Y. Benyamini
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Benyamini, Y. An extension theorem for separable Banach spaces. Israel J. Math. 29, 24–30 (1978). https://doi.org/10.1007/BF02760399

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  • DOI: https://doi.org/10.1007/BF02760399

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