Embeddability of L-1(mu) in dual spaces, geometry of cones and a characterization of c(0)

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:53:57Z
dc.date.available	2014-03-01T01:53:57Z
dc.date.issued	2004	en
dc.identifier.issn	0022-247X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27149
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	L1(GAMMA)	en
dc.title	Embeddability of L-1(mu) in dual spaces, geometry of cones and a characterization of c(0)	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this article we suppose that (Omega, Sigma, mu) is a measure space and T an one-to-one, linear, continuous operator of L-1(mu) into the dual E' of a Banach space E. For any measurable set A consider the image T(L-1(+) (mu(A))) of the positive cone of the space L-1(mu(A)) in E', where mu(A) is the restriction of the measure mu on A. We provide geometrical conditions on the cones T(L-1(+)(mu(A))) Which yield that the measure mu is atomic, i.e., that L-1(mu) is lattice isometric to l(1)(A), where A denotes the set of atoms of mu. This result yields also a new characterization of c(o)(Gamma). (C) 2003 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS	en
dc.identifier.isi	ISI:000187346400011	en
dc.identifier.volume	289	en
dc.identifier.issue	1	en
dc.identifier.spage	126	en
dc.identifier.epage	142	en