A relationship between the space of orthomorphisms and the centre of a vector lattice revisited

Positivity ◽  
2015 ◽  
Vol 20 (2) ◽  
pp. 337-342
Author(s):  
Mohamed Ali Toumi
Keyword(s):  
Vector Lattice

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

2021 ◽  
Vol 78 (1) ◽  
pp. 139-156
Author(s):  
Antonio Boccuto
Keyword(s):  
Optimality Conditions ◽  
Vector Lattice ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Continuous Vector ◽  
Fixed Group ◽  
Composite Functions ◽  
Order Continuous

Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

Order continuous measures

1964 ◽  
Vol 60 (2) ◽  
pp. 205-207 ◽  
Author(s):  
G. T. Roberts
Keyword(s):  
Topological Space ◽  
Linear Form ◽  
Vector Lattice ◽  
Measure Zero ◽  
Continuous Functions ◽  
Order Convergence ◽  
Locally Compact ◽  
Compact Topological Space ◽  
Continuous Measures ◽  
Order Continuous

1. Objective. It is possible to define order convergence on the vector lattice of all continuous functions of compact support on a locally compact topological space. Every measure is a linear form on this vector lattice. The object of this paper is to prove that a measure is such that every set of the first category of Baire has measure zero if and only if the measure is a linear form which is continuous in the order convergence.

scholarly journals Connectedness in some topological vector-lattice groups of sequences

2010 ◽  
Vol 107 (1) ◽  
pp. 150 ◽  
Author(s):  
Lech Drewnowski ◽  
Marek Nawrocki
Keyword(s):  
Banach Space ◽  
Vector Lattice ◽  
Connected Component ◽  
Similar Nature

Let $\eta$ be a strictly positive submeasure on $\mathsf N$. It is shown that the space $\omega(\eta)$ of all real sequences, considered with the topology $\tau_{\eta}$ of convergence in submeasure $\eta$, is (pathwise) connected iff $\eta$ is core-nonatomic. Moreover, for an arbitrary submeasure $\eta$, the connected component of the origin in $\omega(\eta)$ is characterized and shown to be an ideal. Some results of similar nature are also established for general topological vector-lattice groups as well as for the topological vector groups of Banach space valued sequences with the topology $\tau_{\eta}$.

scholarly journals Sequential convergences in a vector lattice

1998 ◽  
Vol 123 (1) ◽  
pp. 33-48
Author(s):  
Ján Jakubík
Keyword(s):  
Vector Lattice

scholarly journals Minimal vector lattice covers

1971 ◽  
Vol 5 (3) ◽  
pp. 331-335 ◽  
Author(s):  
Roger D. Bleier
Keyword(s):  
Vector Lattice ◽  
Lattice Ordered Group ◽  
Ordered Group ◽  
Vector Lattices ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Archimedean Lattice

We show that each archimedean lattice-ordered group is contained in a unique (up to isomorphism) minimal archimedean vector lattice. This improves a result of Paul F. Conrad appearing previously in this Bulletin. Moreover, we show that this relationship between archimedean lattice-ordered groups and archimedean vector lattices is functorial.

scholarly journals Nonsmooth analysis and optimization on partially ordered vector spaces

1992 ◽  
Vol 15 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Thomas W. Reiland
Keyword(s):  
Vector Lattice ◽  
Vector Spaces ◽  
Range Space ◽  
Topological Vector Spaces ◽  
Complete Vector Lattice ◽  
Lipschitz Mappings ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
Complete Vector ◽  
Locally Convex

Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.

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