Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

COMPARABILITY GROUPS

COMPARABILITY GROUPS DEMONSTRATE MATHEMATICAVol. XXXIXNo 12006David J. FoulisCOMPARABILITY GROUPSAbstract. A comparability group is a unital group with a compression base andwith the general comparability property. The additive group of self-adjoint elementsin a von Neumann algebra, and any Dedekind sigma-complete lattice-ordered abeliangroup with order unit are examples of comparability groups. We develop the basic theoryof comparability groups, and show that an archimedean comparability group with theRickart projection property can be embedded in a partially ordered rational vector spacethe elements of which admit a rational spectral resolution.1. IntroductionIn the study of partially ordered abelian interpolation groups with anorder unit, the notion of general comparability plays an important role [8,Chapter 8]. In [3, Definition 4.6], this notion was extended to the class ofcompressible groups, and in [5] a rational spectral resolution theorem wasproved for elements of an archimedean compressible group with both thegeneral comparability and Rickart projection properties. Our purpose inthe present article is to extend the notion of general comparability to amuch wider class of partially ordered abelian groups, namely, unital groupswith a compression base (CB-groups) [7], and to extend the spectral theorydeveloped in [5] to archimedean CB-groups with the general comparabilityand Rickart projection properties.For the reader's convenience, we begin by recalling some http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

COMPARABILITY GROUPS

Foulis, David J.
Demonstratio Mathematica , Volume 39 (1): 18 – Jan 1, 2006
Download PDF
18 pages

Loading next page...
 
/lp/de-gruyter/comparability-groups-0aKLARnLUl

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© by David J. Foulis
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2006-0104
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATE MATHEMATICAVol. XXXIXNo 12006David J. FoulisCOMPARABILITY GROUPSAbstract. A comparability group is a unital group with a compression base andwith the general comparability property. The additive group of self-adjoint elementsin a von Neumann algebra, and any Dedekind sigma-complete lattice-ordered abeliangroup with order unit are examples of comparability groups. We develop the basic theoryof comparability groups, and show that an archimedean comparability group with theRickart projection property can be embedded in a partially ordered rational vector spacethe elements of which admit a rational spectral resolution.1. IntroductionIn the study of partially ordered abelian interpolation groups with anorder unit, the notion of general comparability plays an important role [8,Chapter 8]. In [3, Definition 4.6], this notion was extended to the class ofcompressible groups, and in [5] a rational spectral resolution theorem wasproved for elements of an archimedean compressible group with both thegeneral comparability and Rickart projection properties. Our purpose inthe present article is to extend the notion of general comparability to amuch wider class of partially ordered abelian groups, namely, unital groupswith a compression base (CB-groups) [7], and to extend the spectral theorydeveloped in [5] to archimedean CB-groups with the general comparabilityand Rickart projection properties.For the reader's convenience, we begin by recalling some

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 2006

There are no references for this article.