Archimedean Cones in Vector Spaces

EMELYANOV E.

JOURNAL OF CONVEX ANALYSIS, vol.24, no.1, pp.169-183, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 1
  • Publication Date: 2017
  • Journal Name: JOURNAL OF CONVEX ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.169-183
  • Keywords: Ordered vector space, pre-ordered vector space, Archimedean, Archimedean element, almost Archimedean, Archimedeanization, linear extension
  • Middle East Technical University Affiliated: Yes

Abstract

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+.