Embeddability of L1 (μ) in dual spaces, geometry of cones and a characterization of c0

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:20:23Z
dc.date.available	2014-03-01T01:20:23Z
dc.date.issued	2004	en
dc.identifier.issn	0022247X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15902
dc.subject	banach space	en
dc.subject	Dual Space	en
dc.title	Embeddability of L1 (μ) in dual spaces, geometry of cones and a characterization of c0	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jmaa.2003.08.033	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jmaa.2003.08.033	en
heal.publicationDate	2004	en
heal.abstract	In this article we suppose that (Ω, Σ, μ ) is a measure space and T an one-to-one, linear, continuous operator of L1 (μ) into the dual E′ of a Banach space E. For any measurable set A consider the image T(L1+(μA)) of the positive cone of the space L1(μA) in E′, where μ A is the restriction of the measure μ on A. We provide geometrical conditions on the cones T(L1+(μ A)) which yield that the measure μ is atomic, i.e., that L 1 (μ) is lattice isometric to l1 (A script sign), where A script sign denotes the set of atoms of μ. This result yields also a new characterization of c0(Γ). © 2003 Elsevier Inc. All rights reserved.	en
heal.journalName	Journal of Mathematical Analysis and Applications	en
dc.identifier.doi	10.1016/j.jmaa.2003.08.033	en
dc.identifier.volume	289	en
dc.identifier.issue	1	en
dc.identifier.spage	126	en
dc.identifier.epage	142	en