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 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.

scholarly journals A coincidence theorem in topological vector spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 373-382 ◽  
Author(s):  
Olga Hadžić
Keyword(s):  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
Coincidence Theorem ◽  
Locally Convex ◽  
Special Case

In this paper we prove a coincidence theorem in not necessarily locally convex topological vector spaces, which contains, as a special case, a coincidence theorem proved by Felix Browder. As an application, a result about the existence of maximal elements is obtained.

scholarly journals On the stability of barrelled topologies, I

1979 ◽  
Vol 20 (3) ◽  
pp. 385-395 ◽  
Author(s):  
W.J. Robertson ◽  
F.E. Yeomans
Keyword(s):  
Dual Space ◽  
Vector Spaces ◽  
Mackey Topology ◽  
Topological Vector Spaces ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Countable Dimension ◽  
The Stability ◽  
Locally Convex ◽  
Barrelled Space

This note investigates, for locally convex topological vector spaces, the question of how far the property of being barrelled is stable under small increase in the size of the dual space. If the dual F of a barrelled space E is enlarged by a finite dimensional vector space M, then E remains barrelled under the new Mackey topology τ(E, F+M). We discuss what happens when M has countable dimension.

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 +∞.

scholarly journals ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS

2008 ◽  
Vol 50 (2) ◽  
pp. 271-288
Author(s):  
HELGE GLÖCKNER
Keyword(s):  
Differential Calculus ◽  
Vector Spaces ◽  
Local Convexity ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
General Curve ◽  
Infinite Dimensional Analysis ◽  
Locally Convex ◽  
Differentiability Properties ◽  
Made In

AbstractThe General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. In this article, we generalize the General Curve Lemma in two ways. First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.

scholarly journals Linear mappings between topological vector spaces

1972 ◽  
Vol 14 (1) ◽  
pp. 105-118
Author(s):  
B. D. Craven
Keyword(s):  
Inductive Limit ◽  
Vector Spaces ◽  
Continuous Linear ◽  
Additional Structure ◽  
Normed Spaces ◽  
Topological Vector Spaces ◽  
Locally Convex

If A and B are locally convex topological vector spaces, and B has certain additional structure, then the space L(A, B) of all continuous linear mappings of A into B is characterized, within isomorphism, as the inductive limit of a family of spaces, whose elements are functions, or measures. The isomorphism is topological if L(A, B) is given a particular topology, defined in terms of the seminorms which define the topologies of A and B. The additional structure on B enables L(A, B) to be constructed, using the duals of the normed spaces obtained by giving A the topology of each of its seminorms separately.

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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