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Archimedean Cones in Vector Spaces
Date
2017-01-01
Author
Emelyanov, Eduard
Metadata
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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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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.