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() consisting of all bounded, countably supported functions on a set embeds isomorphically into l if and only if it does not contain isometric copies of c0(1). Moreover, a subspace of lc(1) 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(1)).

authors

• Johnson, William

published proceedings

• MATHEMATISCHE NACHRICHTEN

author list (cited authors)

• Johnson, W. B., & Kania, T.

citation count

• 2

complete list of authors

• Johnson, William B||Kania, Tomasz

publication date

• September 2019

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

start page

• 2028

end page

• 2031

volume

• 292

issue

• 9

URL

• http://dx.doi.org/10.1002/mana.201800308