Archimedean Cones in Vector Spaces

EMELYANOV E.

JOURNAL OF CONVEX ANALYSIS, cilt.24, sa.1, ss.169-183, 2017 (SCI-Expanded) identifier

  • 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+.