Necessary and Sufficient Conditions for the Order- Completeness of Partially Ordered Vector Spaces

1978 ◽  
Vol 81 (1) ◽  
pp. 301-311 ◽  
Author(s):  
Karl-Heinz Elster ◽  
Reinhard Nehse
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Vector Spaces ◽  
Partially Ordered ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
Order Completeness ◽  
Necessary And Sufficient

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 A unifying approach for some nonexpansiveness conditions on modular vector spaces

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Andrea Bejenaru ◽  
Mihai Postolache
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Vector Spaces ◽  
Minimizing Sequences ◽  
Ishikawa Iteration ◽  
New Class ◽  
Condition C ◽  
Necessary And Sufficient

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

scholarly journals Extensions of strict partial orders in N-Groups

1978 ◽  
Vol 25 (2) ◽  
pp. 241-249 ◽  
Author(s):  
K. B. Prabhakara Rao
Keyword(s):  
Partial Order ◽  
Sufficient Conditions ◽  
Partial Orders ◽  
Necessary And Sufficient Conditions ◽  
Full Extension ◽  
Partially Ordered ◽  
Strict Partial Order ◽  
Positive Elements ◽  
Necessary And Sufficient

AbstractAn attempt is made to extend the theory of extensions of partial orders in groups to strict partially ordered N-groups. Necessary and sufficient conditions, for a strict partial order of an N-group to have a strict full extension, and for a strict partial order of an N-group to be an intersection of strict full orders, are obtained when the partially ordered near-ring N and the N-group G satisfy the condition (− x) n = − xn for all elements x in G and positive elements n in N.

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.

The order completeness of some spaces of vector-valued functions

1974 ◽  
Vol 11 (1) ◽  
pp. 57-61 ◽  
Author(s):  
Donald I. Cartwright
Keyword(s):  
Banach Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Banach Lattices ◽  
Nuclear Operators ◽  
Order Completeness ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Order Intervals ◽  
Vector Valued

Let E be a Banach lattice. Necessary and sufficient conditions are given for the order completeness of the Banach lattices C(X, E) and L1(μ, E) in terms of the compactness of the order intervals in E. The results have interpretations in terms of spaces of compact and nuclear operators.

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.

Sign in / Sign up

Export Citation Format

Share Document