# 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

15 pages

/lp/springer-journals/on-self-majorizing-elements-in-archimedean-vector-lattices-q98ElcKx0p
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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create folders to

Export folders, citations