A relationship between the space of orthomorphisms and the centre of a vector lattice

A relationship between the space of orthomorphisms and the centre of a vector lattice When are so happy in a vector lattice that all band preserving linear operators turn out to be in the ideal centre? This question was raised by Wickstead (Representation and duality in Representation and duality Riesz spaces. Compos Math 35(3):225–238, 1977) (though not explicitly stated) and by the first author and Chil and Meyer (On the centre of a vector lattice. Indag Math 23:167–183, 2012). The answer depends on the vector lattice in which the operator in question acts. However, in this article we focus our attention on this question. First, we give a complete description of those vector lattices $$E$$ E with the property that every orthomorphism on $$E$$ E is a central operator. Secondly, we provide a counterexample to the main result, about Wickstead’s question, in a recent paper of Toumi [see Theorem 3, When orthomorphisms are in the ideal center, in Positivity (2014, in press). (Published online: 11 Dec 2013)]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A relationship between the space of orthomorphisms and the centre of a vector lattice

Loading next page...
 
/lp/springer_journal/a-relationship-between-the-space-of-orthomorphisms-and-the-centre-of-a-orXh0yqV2j
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/s11117-014-0308-2
Publisher site
See Article on Publisher Site

Abstract

When are so happy in a vector lattice that all band preserving linear operators turn out to be in the ideal centre? This question was raised by Wickstead (Representation and duality in Representation and duality Riesz spaces. Compos Math 35(3):225–238, 1977) (though not explicitly stated) and by the first author and Chil and Meyer (On the centre of a vector lattice. Indag Math 23:167–183, 2012). The answer depends on the vector lattice in which the operator in question acts. However, in this article we focus our attention on this question. First, we give a complete description of those vector lattices $$E$$ E with the property that every orthomorphism on $$E$$ E is a central operator. Secondly, we provide a counterexample to the main result, about Wickstead’s question, in a recent paper of Toumi [see Theorem 3, When orthomorphisms are in the ideal center, in Positivity (2014, in press). (Published online: 11 Dec 2013)].

Journal

PositivitySpringer Journals

Published: Sep 16, 2014

References

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
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off