On self-majorizing elements in Archimedean vector lattices

On self-majorizing elements in Archimedean vector lattices A finite element in an Archimedean vector lattice is called self-majorizing if its modulus is a majorant. Such elements exist in many vector lattices and naturally occur in different contexts. They are also known as semi-order units as the modulus of a self-majorizing element is an order unit in the band generated by the element. In this paper the properties of self-majorizing elements are studied systematically, and the relations between the sets of finite, totally finite and self-majorizing elements of a vector lattice are provided. In a Banach lattice an element $$\varphi $$ φ is self-majorizing , if and only if the ideal and the band both generated by $$\varphi $$ φ coincide. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On self-majorizing elements in Archimedean vector lattices

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Publisher
Springer Basel
Copyright
Copyright © 2014 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-014-0278-4
Publisher site
See Article on Publisher Site

Abstract

A finite element in an Archimedean vector lattice is called self-majorizing if its modulus is a majorant. Such elements exist in many vector lattices and naturally occur in different contexts. They are also known as semi-order units as the modulus of a self-majorizing element is an order unit in the band generated by the element. In this paper the properties of self-majorizing elements are studied systematically, and the relations between the sets of finite, totally finite and self-majorizing elements of a vector lattice are provided. In a Banach lattice an element $$\varphi $$ φ is self-majorizing , if and only if the ideal and the band both generated by $$\varphi $$ φ coincide.

Journal

PositivitySpringer Journals

Published: Feb 12, 2014

References

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