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

abstract

• © 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)).

authors

• Johnson, William

author list (cited authors)

• Johnson, W. B., & Kania, T.

citation count

• 1

publication date

• January 1, 2019 11:11 AM

publisher

• Wiley  Publisher

published in

• MATHEMATISCHE NACHRICHTEN  Journal

keywords

• Banach Space
• Countably Supported
• Long Unconditional Basis
• Wcg Space
• Wld Space

Digital Object Identifier (DOI)

• 10.1002/mana.201800308