Archimedean Cones in Vector Spaces

Date

2017-01-01

Author

Emelyanov, Eduard

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

277
views

0
downloads

In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by Paulsen and Tomforde [4]. We present a general version of the Archimedeanization which covers arbitrary OVS. Also we show that an OVS (V, V+) is Archimedean if and only if inf(tau is an element of{tau}), y is an element of L(x(tau) - y) = 0 for any bounded below decreasing net {x(tau)}(tau) in V, where L is the collection of all lower bounds of {x(tau)}(tau), and give characterization of the almost Archimedean property of V+ in terms of existence of a linear extension of an additive mapping T : U+ -> V+.

Subject Keywords

Ordered vector space, Pre-ordered vector space, Archimedean, Archimedean element, Almost Archimedean, Archimedeanization, Linear extension

URI

https://hdl.handle.net/11511/55220

Journal

JOURNAL OF CONVEX ANALYSIS

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Series solution of the wave equation in optic fiber Çıldır, Sema; Çakır, Serhat; Department of Physics (2007) In this study, the mapped Galerkin method was applied to solve the vector wave equation based on H field and to obtain the propagation constant in x y space. The vector wave equation was solved by the transformation of the infinite x y plane onto a unit square. Two-dimensional Fourier series expansions were used in the solutions. Modal fields and propagation constants of dielectric waveguides were calculated. In the first part of the study, all of the calculations were made in step index fibers. Transvers...
Exact solutions of the radial Schrodinger equation for some physical potentials IKHDAİR, SAMEER; Sever, Ramazan (2007-12-01) By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.
Nonstandard hulls of lattice-normed ordered vector spaces Aydin, Abdullah; Gorokhova, Svetlana; Gul, Hasan (2018-01-01) Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.
Annulus criteria for mixed nonlinear elliptic differential equations ŞAHİNER, YETER; Zafer, Ağacık (Elsevier BV, 2011-05-01) New oscillation criteria are obtained for forced second order elliptic partial differential equations with damping and mixed nonlinearities of the form
uτ-Convergence in locally solid vector lattices Dabboorasad, Yousef A M; Emel’yanov, Eduard; Department of Mathematics (2018) We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if

Citation Formats

E. Emelyanov, “Archimedean Cones in Vector Spaces,” JOURNAL OF CONVEX ANALYSIS, pp. 169–183, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55220.