A p-theory of ordered normed spaces

A p-theory of ordered normed spaces We propose a pair of axioms (O.p.1) and (O.p.2) for 1 ≤ p ≤ ∞ and initiate a study of a (matrix) ordered space with a (matrix) norm, in which the (matrix) norm is related to the (matrix) order. We call such a space a (matricially) order smooth p-normed space. The advantage of studying these spaces over L p -matricially Riesz normed spaces is that every matricially order smooth ∞-normed space can be order embedded in some C*-algebra. We also study the adjoining of an order unit to a (matricially) order smooth ∞-normed space. As a consequence, we sharpen Arveson’s extension theorem of completely positive maps. Another combination of these axioms yields an order theoretic characterization of the set of real numbers amongst ordered normed linear spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A p-theory of ordered normed spaces

Positivity , Volume 14 (3) – Jul 31, 2009

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SP Birkhäuser Verlag Basel
Copyright © 2009 by Birkhäuser Verlag Basel/Switzerland
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
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