Lattice-Subspaces of C[0,1] and Positive Bases

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:09:57Z
dc.date.available	2014-03-01T01:09:57Z
dc.date.issued	1994	en
dc.identifier.issn	0022-247X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11263
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.title	Lattice-Subspaces of C[0,1] and Positive Bases	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jmaa.1994.1178	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jmaa.1994.1178	en
heal.language	English	en
heal.publicationDate	1994	en
heal.abstract	A closed vector subspace of a vector lattice E is a lattice-subspace of E if X with the induced ordering is a vector lattice in its own right-but not necessarily a vector sublattice. In this work, we remark that C[0, 1] is a universal Banach lattice in the sense that every separable Banach lattice is order-isomorphic to a closed lattice-subspace of C[0, 1]. In addition, we show that (up to an order-isomorphism) if a closed lattice-subspace of C[0, 1] has a positive basis (bn), then for each n there exists a subinterval Jn on which bn is positive and every other element of this basis vanishes. By means of our main result, we present necessary and sufficient conditions that guarantee the existence of positive bases in an arbitrary lattice-subspace of C[0, 1]. These results are related to the general existence problem of positive bases in Banach lattices as well as the existence of unconditional bases in Banach spaces. © 1994 Academic Press. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS	en
heal.journalName	Journal of Mathematical Analysis and Applications	en
dc.identifier.doi	10.1006/jmaa.1994.1178	en
dc.identifier.isi	ISI:A1994NQ16500001	en
dc.identifier.volume	184	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	18	en