scholarly journals Nonsmooth analysis on partially ordered vector spaces. I. Convex case

1983 ◽  
Vol 107 (2) ◽  
pp. 403-458 ◽  
Author(s):  
Nikolaos Papageorgiou
Keyword(s):  
Nonsmooth Analysis ◽  
Vector Spaces ◽  
Partially Ordered ◽  
Convex Case ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces

scholarly journals On the Biadjoint of Riesz-like homomorphisms on partially ordered vector spaces

1997 ◽  
Vol 56 (3) ◽  
pp. 473-481
Author(s):  
Gerard Buskes ◽  
Jamie Summerville
Keyword(s):  
Vector Spaces ◽  
New Technique ◽  
Partially Ordered ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
A New Technique

We generalise to partially ordered vector spaces, with a new technique, Arendt's approach to Kim's characterisation of Riesz homomorphisms.

scholarly journals Integral representation theorems in partially ordered vector spaces

1991 ◽  
Vol 51 (2) ◽  
pp. 187-215 ◽  
Author(s):  
Panaiotis K. Pavlakos
Keyword(s):  
Integral Representation ◽  
Quantum Probability ◽  
Jordan Algebras ◽  
Vector Spaces ◽  
Type I ◽  
Representation Theorems ◽  
Partially Ordered ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
Set Function

AbstractDefining a Radon-type integration process we extend the Alexandroff, Fichtengolts-KantorovichHildebrandt and Riesz integral representation theorems in partially ordered vector spaces.We also identify some classes of operators with other classes of operator-valued set functions, the correspondence between operator and operator-valued set function being given by integration.All these established results can be immediately applied in C* -algebras (especially in W* -algebras and AW* -algebras of type I), in Jordan algebras, in partially ordered involutory (O*-)algebras, in semifields, in quantum probability theory, as well as in the operator Feynman-Kac formula.

Minimal decompositions in partially ordered normed vector spaces

1968 ◽  
Vol 64 (4) ◽  
pp. 989-1000 ◽  
Author(s):  
A. J. Ellis
Keyword(s):  
Positive Cone ◽  
Intersection Property ◽  
Vector Spaces ◽  
Partially Ordered ◽  
Base Section ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
Minimal Decomposition ◽  
Normed Vector

In this paper we study partially ordered vector spaces X whose positive cone K possesses a base which defines a norm in X. A positive decomposition x = y − z of the element x is said to be minimal if ‖x‖ = ‖y‖ + ‖z‖. We proved in (6) that the property that every element of X has a unique minimal decomposition is equivalent to an intersection property for homothetic translates of the base. Section 2 of the present paper analyses this intersection property in much more detail and discusses possible generalizations of it.

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