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Embedding Banach spaces into the space of bounded functions with countable support

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  • William B. Johnson
  • Tomasz Kania

Abstract

We prove that a WLD subspace of the space ℓ∞c(Γ) consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into ℓ∞ if and only if it does not contain isometric copies of c0(ω1). Moreover, a subspace of ℓ∞c(ω1) is constructed that has an unconditional basis, does not embed into ℓ∞, and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of c0(ω1)).

Suggested Citation

  • William B. Johnson & Tomasz Kania, 2019. "Embedding Banach spaces into the space of bounded functions with countable support," Mathematische Nachrichten, Wiley Blackwell, vol. 292(9), pages 2028-2031, September.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:9:p:2028-2031
    DOI: 10.1002/mana.201800308
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