Archimedean Cones in Vector Spaces

Date

2017-01-01

Author

Emelyanov, Eduard

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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+.

Subject Keywords

Ordered vector space, Pre-ordered vector space, Archimedean, Archimedean element, Almost Archimedean, Archimedeanization, Linear extension

URI

https://hdl.handle.net/11511/55220

Journal

JOURNAL OF CONVEX ANALYSIS

Collections

Department of Mathematics, Article

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Citation Formats

E. Emelyanov, “Archimedean Cones in Vector Spaces,” JOURNAL OF CONVEX ANALYSIS, pp. 169–183, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55220.