Nonstandard hulls of ordered vector spaces

Date

2016-06-01

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

192
views

0
downloads

This paper undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated.

Subject Keywords

Ordered vector space, Krein space, Nonstandard extension, Nonstandard hull, LATTICES

URI

https://hdl.handle.net/11511/40572

Journal

POSITIVITY

DOI

https://doi.org/10.1007/s11117-015-0364-2

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Nonstandard hulls of ordered vector spaces Gül, Hasan; Emel'yanov, Eduard; Department of Mathematics (2015) This thesis undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated
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.
ON GENERALIZED LOCAL SYMMETRIES OF THE SO(2,1) INVARIANT NONLINEAR SIGMA-MODEL BASKAL, S; ERIS, A; SATIR, A (1994-12-19) The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
Noncommutative affine spaces and Lie-complete rings Dosi, Anar (2015-02-01) In this paper, we investigate the structure sheaves of an (infinite-dimensional) affine NC-space A(nc)(x) affine Lie-space A(lich)(x), and their nilpotent perturbations A(nc,q)(x) and A(lich),(x)(q) respectively. We prove that the schemes A(nc)(x) and A(lich)(x) are identical if and only if x is a finite set of variables, that is, when we deal with finite-dimensional noncommutative affine spaces. For each (Zariski) open subset U subset of X = Spec(C vertical bar x vertical bar), we obtain the precise descri...
Hilbert functions of gorenstein monomial curves Topaloğlu Mete, Pınar; Arslan, Sefa Feza; Department of Mathematics (2005) The aim of this thesis is to study the Hilbert function of a one-dimensional Gorenstein local ring of embedding dimension four in the case of monomial curves. We show that the Hilbert function is non-decreasing for some families of Gorenstein monomial curves in affine 4-space. In order to prove this result, under some arithmetic assumptions on generators of the defining ideal, we determine the minimal generators of their tangent cones by using the standard basis and check the Cohen-Macaulayness of them. Lat...

Citation Formats

E. Emelyanov, “Nonstandard hulls of ordered vector spaces,” POSITIVITY, pp. 413–433, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40572.