The Structure of Lattice-Subspaces

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:19:38Z
dc.date.available	2014-03-01T01:19:38Z
dc.date.issued	2003	en
dc.identifier.issn	1385-1292	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15625
dc.subject	banach lattice	en
dc.subject.classification	Mathematics	en
dc.subject.other	PORTFOLIO INSURANCE	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	BASES	en
dc.subject.other	L1	en
dc.title	The Structure of Lattice-Subspaces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1023/A:1025872101176	en
heal.identifier.secondary	http://dx.doi.org/10.1023/A:1025872101176	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	In Polyrakis (1983; Math. Proc. Cambridge Phil. Soc. 94, 519) it is proved that each infinite-dimensional, closed lattice-subspace of ℓ1 is order-isomorphic to ℓ1 and in Polyrakis (1987; Math. Anal. Appl. 184, 1) that each separable Banach lattice is order isomorphic to a closed lattice-subspace of C [0, 1]. Therefore ℓ1 contains only one lattice-subspace but C [0, 1] contains all the separable Banach lattices. In the first section of this article we study the kind of the order embeddability of a separable Banach lattice in C[0, 1]. We show that the AM spaces have the ""best"" behavior and the AL-spaces the ""worst"". In the second section we prove that the closure of a lattice-subspace is not necessarily a lattice-subspace and in the least one we study lattice-subspaces with positive bases.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	Positivity	en
dc.identifier.doi	10.1023/A:1025872101176	en
dc.identifier.isi	ISI:000185516300002	en
dc.identifier.volume	7	en
dc.identifier.issue	1-2	en
dc.identifier.spage	23	en
dc.identifier.epage	32	en