ordered vector space
Recently Published Documents


TOTAL DOCUMENTS

24
(FIVE YEARS 0)

H-INDEX

8
(FIVE YEARS 0)

2016 ◽  
Vol 12 (4) ◽  
pp. 6160-6170
Author(s):  
Antonio Boccuto

We give a direct proof of sandwich-type theorems for linear invariant partially ordered vector space operators in the setting of convexity. As consequences, we deduce equivalence results between sandwich, Hahn-Banach, separation and Krein-type extension theorems, Fenchel duality, Farkas and Kuhn-Tucker-type minimization results and subdifferential formulas in the context of invariance. As applications, we give Tarski-type extension theorems and related examples for vector lattice-valued invariant probabilities, defined on suitable kinds of events.



2016 ◽  
Vol 101 (2) ◽  
pp. 277-287
Author(s):  
AARON TIKUISIS

It is shown that, for any field $\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of $\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages $(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (where $n$ does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with $\mathbb{F}$ replaced by the integers, $\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with $\mathbb{Q}$.



Positivity ◽  
2015 ◽  
Vol 20 (4) ◽  
pp. 877-916 ◽  
Author(s):  
A. C. M. van Rooij ◽  
W. B. van Zuijlen


2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Toshiharu Kawasaki ◽  
Masashi Toyoda ◽  
Toshikazu Watanabe

Using a fixed point theorem in a partially ordered set, we give a new proof of the Hahn-Banach theorem in the case where the range space is a partially ordered vector space.





2007 ◽  
Vol 72 (4) ◽  
pp. 1108-1140 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Sergei Starchenko

AbstractLet M = 〈M, +, <, 0, {λ}λЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L.





2001 ◽  
Vol 354 (5) ◽  
pp. 2055-2077 ◽  
Author(s):  
Charalambos D. Aliprantis ◽  
Rabee Tourky


Sign in / Sign up

Export Citation Format

Share Document