Archimedean Cones in Vector Spaces
JOURNAL OF CONVEX ANALYSIS, cilt.24, sa.1, ss.169-183, 2017 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 1
- Basım Tarihi: 2017
- Dergi Adı: JOURNAL OF CONVEX ANALYSIS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.169-183
- Anahtar Kelimeler: Ordered vector space, pre-ordered vector space, Archimedean, Archimedean element, almost Archimedean, Archimedeanization, linear extension
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by Paulsen and Tomforde [4]. We present a general version of the Archimedeanization which covers arbitrary OVS. Also we show that an OVS (V, V+) is Archimedean if and only if inf(tau is an element of{tau}), y is an element of L(x(tau) - y) = 0 for any bounded below decreasing net {x(tau)}(tau) in V, where L is the collection of all lower bounds of {x(tau)}(tau), and give characterization of the almost Archimedean property of V+ in terms of existence of a linear extension of an additive mapping T : U+ -> V+.