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

William B. Johnson and Tomasz Kania

Mathematische Nachrichten, 2019, vol. 292, issue 9, 2028-2031

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)).

Date: 2019
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https://doi.org/10.1002/mana.201800308

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