Embedding Banach spaces into the space of bounded functions with countable support
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Â© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim We prove that a WLD subspace of the space lcâˆž(Î“) consisting of all bounded, countably supported functions on a set Î“ embeds isomorphically into lâˆž if and only if it does not contain isometric copies of c0(Ï‰1). Moreover, a subspace of lcâˆž(Ï‰1) is constructed that has an unconditional basis, does not embed into lâˆž, and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of c0(Ï‰1)).
author list (cited authors)
Johnson, W. B., & Kania, T.