Toggle navigation
Search
Browse
EKT item types
Institutions
Collections
Interoperability
Info
The project
Help
For institutions
Contribute
Publication Requirements
Expression of Interest Form
Contact
ΕΛ
•
ΕΝ
In all fields
Subject
Type
Location
Title
Time
Creator/contributor
×
+
Search
Clear
Help
Lattice-Subspaces of C[0,1] and Positive Bases
This item is provided by the institution :
National Technical University of Athens
Repository :
Digital Library of National Technical University of Athens | Dspace@NTUA
see the original item page
in the repository's web site and access all digital files if the item
*
share
Semantic enrichment by EKT
ΕΚΤ item type
Journal part
(EN)
Scientific article
(EN)
EKT year
1994
(EN)
EKT historical period
Title
Lattice-Subspaces of C[0,1] and Positive Bases (EN)
Creator
Polyrakis, IA (EN)
Description
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)
Type
journalArticle (EN)
Subject
Mathematics (EN)
Mathematics, Applied (EN)
Provider
National Technical University of Athens
Repository / collection
Digital Library of National Technical University of Athens | Dspace@NTUA
Subcollections
Κεντρική Βιβλιοθήκη Ε.Μ.Π.
Ιδρυματικό Αποθετήριο
Δημοσιεύσεις μελών Δ.Ε.Π. σε περιοδικά
Journal
Journal of Mathematical Analysis and Applications (EN)
Language
English
Issued
1994 (EN)
Identifier
http://hdl.handle.net/123456789/11263
10.1006/jmaa.1994.1178 (EN)
1 (EN)
18 (EN)
0022-247X (EN)
ISI:A1994NQ16500001 (EN)
184 (EN)
Publisher
ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS (EN)
*
Institutions are responsible for keeping their URLs functional (digital file, item page in repository site)
×
×
Βοηθείστε μας να κάνουμε καλύτερο το
OpenArchives
.gr
.
Πάρτε μέρος στη σύντομη έρευνα!