Embedding Properties of Locally Convex Riesz Spaces

1996 ◽  
pp. 171-186
Author(s):  
Yau-chuen Wong
Keyword(s):  
Riesz Spaces ◽  
Locally Convex

scholarly journals Порядково борнологические локально выпуклые решеточные конусы

2017 ◽  
Author(s):  
D. Ayaseh ◽  
A. Ranjbari
Keyword(s):  
Convex Cones ◽  
Riesz Spaces ◽  
Convex Lattice ◽  
Locally Convex Cones ◽  
Lattice Cones ◽  
Locally Convex ◽  
Special Case

In this paper, we introduce the concepts of $us$-lattice cones and order bornological locally convex lattice cones. In the special case of locally convex solid Riesz spaces, these concepts reduce to the known concepts of seminormed Riesz spaces and order bornological Riesz spaces, respectively. We define solid sets in locally convex cones and present some characterizations for order bornological locally convex lattice cones.

The order-bound topology on Riesz spaces

1970 ◽  
Vol 67 (3) ◽  
pp. 587-593 ◽  
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Convex Sets ◽  
Vector Lattice ◽  
Positive Cone ◽  
Riesz Space ◽  
Hausdorff Topology ◽  
Riesz Spaces ◽  
Neighbourhood Base ◽  
Solid Hull ◽  
Locally Convex

1. Introduction. Let (X, C) be a Riesz space (or vector lattice) with positive cone C. A subset B of X is said to be solid if it follows from |x| ≤ |b| with b in B that x is in B (where |x| denotes the supremum of x and − x). The solid hull of B (absolute envelope of B in the terminology of Roberts (2)) is denoted to be the smallest solid set containing B, and is denoted by SB. A locally convex Hausdorff topology on (X, C) is called a locally solid topology if admits a neighbourhood-base of 0 consisting of solid and convex sets in X; and (X, C, ), where is a locally solid topology, is called a locally convex Riesz space.

scholarly journals A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1512
Author(s):  
Juan Luis García Guirao ◽  
Mobashir Iqbal ◽  
Zia Bashir ◽  
Tabasam Rashid
Keyword(s):  
Riesz Space ◽  
Linear Operators ◽  
Separation Property ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Spaces ◽  
Fuzzy Order ◽  
Locally Convex ◽  
Special Case

This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.

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