Weak compactness of direct sums in locally convex cones

2018 ◽  
Vol 55 (4) ◽  
pp. 487-497
Author(s):  
Mohammad Reza Motallebi
Keyword(s):  
Weak Compactness ◽  
Convex Cones ◽  
Weakly Compact ◽  
Direct Sums ◽  
Direct Sum ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Compact Subsets

We discuss the weakly compact subsets of direct sum cones for the upper, lower and symmetric topologies and investigate the X-topologies of the weak upper, lower and sym-metric compact subsets of direct sum cones on product cones.

Products and Direct Sums in Locally Convex Cones

2012 ◽  
Vol 55 (4) ◽  
pp. 783-798 ◽  
Author(s):  
M. R. Motallebi ◽  
H. Saiflu
Keyword(s):  
Convex Cones ◽  
Direct Sums ◽  
Lower Upper ◽  
Direct Sum ◽  
Locally Convex Cones ◽  
Locally Convex

AbstractIn this paper we define lower, upper, and symmetric completeness and discuss closure of the sets in products and direct sums. In particular, we introduce suitable bases for these topologies, which leads us to investigate completeness of the direct sum and its components. Some results obtained about X-topologies and polars of the neighborhoods.

Weak compactness in locally convex cones

Positivity ◽  
2018 ◽  
Vol 23 (2) ◽  
pp. 303-313
Author(s):  
M. R. Motallebi
Keyword(s):  
Weak Compactness ◽  
Convex Cones ◽  
Locally Convex Cones ◽  
Locally Convex

Weak Compactness and Separation

1964 ◽  
Vol 16 ◽  
pp. 204-206 ◽  
Author(s):  
Robert C. James
Keyword(s):  
Banach Space ◽  
Weak Compactness ◽  
The Other ◽  
Weakly Compact ◽  
Linear Spaces ◽  
Topological Linear ◽  
Locally Convex ◽  
Compact Subsets

The purpose of this paper is to develop characterizations of weakly compact subsets of a Banach space in terms of separation properties. The sets A and B are said to be separated by a hyperplane H if A is contained in one of the two closed half-spaces determined by H, and B is contained in the other; A and B are strictly separated by H if A is contained in one of the two open half-spaces determined by H, and B is contained in the other. The following are known to be true for locally convex topological linear spaces.

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

scholarly journals Completeness on locally convex cones

2014 ◽  
Vol 352 (10) ◽  
pp. 785-789 ◽  
Author(s):  
Mohammad Reza Motallebi
Keyword(s):  
Convex Cones ◽  
Locally Convex Cones ◽  
Locally Convex

scholarly journals Duality on locally convex cones

2008 ◽  
Vol 337 (2) ◽  
pp. 888-905 ◽  
Author(s):  
M.R. Motallebi ◽  
H. Saiflu
Keyword(s):  
Convex Cones ◽  
Locally Convex Cones ◽  
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.

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