Finitely Generated Vector Sublattices View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1998

AUTHORS

Charles B. Huijsmans

ABSTRACT

Let E+ be the positive cone of an Archimedean vector lattice E. It is shown in [4, Theorem 2.1] that for arbitrary u, v ∈ E+ the vector sublattice R(u, v) of E generated by u and v can be described as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ R\left( {u,\upsilon } \right) = Span\left\{ {{{{\left( {\alpha u + \beta \upsilon } \right)}}^{ + }}:\alpha \beta \in \mathbb{R}} \right\}. $$\end{document}.We will demonstrate in this paper that this result no longer holds for three or more positive elements. It also ceases to be true for the vector sublattice generated by two (or more) arbitrary elements. Moreover, we will show that every finitely generated vector sublattice of E is finite-dimensional if and only if E is hyper-Archimedean. More... »

PAGES

79-95

Book

TITLE

Functional Analysis and Economic Theory

ISBN

978-3-642-72224-0
978-3-642-72222-6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-72222-6_7

DOI

http://dx.doi.org/10.1007/978-3-642-72222-6_7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019422947


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