Embedding Banach spaces into the space of bounded functions with countable support
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abstract
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© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim We prove that a WLD subspace of the space lc∞(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 lc∞(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)).
author list (cited authors)
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Johnson, W. B., & Kania, T.
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Johnson, William B||Kania, Tomasz
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keywords
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Banach Space
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Countably Supported
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Long Unconditional Basis
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Wcg Space
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Wld Space
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