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Equivalent norms on spaces of bounded functions

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Abstract

Let ω1 denote the first uncountable ordinal,m ω(ω1) the Banach space of all bounded real functions on ω1 with countable support (with the supremum norm). It is shown that any space isomorphic tom ω(ω1) contains a subspace isometric tom ω(ω1). Several similar results concerning higher cardinals are obtained.

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Authors and Affiliations

  1. Trinity College, CB2 1TQ, Cambridge, England

    J. R. Partington

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  1. J. R. Partington
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Partington, J.R. Equivalent norms on spaces of bounded functions. Israel J. Math. 35, 205–209 (1980). https://doi.org/10.1007/BF02761190

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  • DOI: https://doi.org/10.1007/BF02761190

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