Nonstandard hulls of vector lattices
type: Item
instance of: scholarly article
title: Nonstandard hulls of vector lattices
zbMATH Open document ID: 0899.46072
DOI: 10.1007/BF02104943
published in: Siberian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: The author defines the nonstandard hull \(\overline E\) of a vector lattice \(E\) in an analogous way to the usual definition of the nonstandard hull \(\widetilde V\) of a normed vector space \(V\), whereas the absolute value on \(E\) replaces the role of the norm on \(V\). For a normed vector lattice \(E\), he compares \(\overline E\) and \(\widetilde E\). He also investigates a situation where \(E\) is lattice isomorphic to \(\overline E\) and calculates the nonstandard hull of several examples. The reviewer remarks that an alternative to the author's definition is offered via an ultrapower construction [the reviewer and \textit{A. C. M. van Rooij}, Compos. Math. 83, No. 3, 311-327 (1992; Zbl 0781.46009)]. In the latter alternative, the nonstandard hull of any Archimedean vector lattice is Archimedean, thus avoiding the question at the end of this paper.
Mathematics Subject Classification ID: 46S20
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 794617
zbMATH Keywords: nonstandard
zbMATH Keywords: vector lattice
zbMATH Keywords: ultrapower construction
author: Eduard Yu. Emel'yanov
reviewed by: Gerard Buskes
MaRDI profile type: Publication
cites work: Q3825006
cites work: Q5719719
cites work: Q4711784
cites work: Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles
cites work: On a constrained variational problem and the space of horizontal paths
full work available at URL: https://doi.org/10.1007/bf02104943
OpenAlex ID: W2046838141
description: scientific article; zbMATH DE number 794617