scholarly journals Hahn-Banach Type Theorems for Locally Convex Cones

2000 ◽  
Vol 68 (1) ◽  
pp. 104-125 ◽  
Author(s):  
Walter Roth
Keyword(s):  
Convex Cones ◽  
Vector Spaces ◽  
Linear Functionals ◽  
Sandwich Theorem ◽  
Locally Convex Cones ◽  
Sublinear Functionals ◽  
Locally Convex ◽  
Separation Results

AbstractWe prove Hahn-Banach type theorems for linear functionals with values in R∪{+∞} on ordered cones, Using the concept of locally convex cones, we provide a sandwich theorem involving sub- and superlinear functionals which are allowed to attain infinite values. It render general versions of well-known extension and separation results. We describe the range of all linear functionals sandwiched between given sub- and superlinear functionals on an ordered cone. The results are of interest even in vector spaces, since we consider sublinear functionals that may attain the value +∞.

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 An introduction to locally convex cones

2017 ◽  
Vol 16 (1) ◽  
Author(s):  
Walter Roth
Keyword(s):  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Locally Convex Cones ◽  
Locally Convex

This survey introduces and motivates  the foundations  of the theory oflocally convex cones which aims to generalize the well established theory of locally convex topological vector spaces. We explain the main concepts,provide definitions, principal results, examples and applications. For details and proofs we generally refer to the literature.

scholarly journals Extending Edgar's ordering to locally convex spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 175-188
Author(s):  
Neill Robertson
Keyword(s):  
Convex Space ◽  
Dual Pair ◽  
Locally Convex Space ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Hausdorff Topological Vector Space ◽  
Locally Convex ◽  
Mackey Topologies

By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.

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.

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 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.

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