Band Decompositions for Disjointness Preserving Operators

Band Decompositions for Disjointness Preserving Operators Positivity 4: 259–288, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. Band Decompositions for Disjointness Preserving Operators 1 2 B. DE PAGTER and A.R. SCHEP Department of Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA 1. Introduction Let E and F be Riesz spaces with F Dedekind complete and let T;S V E ! F be order bounded linear disjointness preserving operators. The main problem we discuss in this paper is to find conditions on either T and S, or the space E,so that the property that T and S are disjoint in the space or order bounded operators from E into F , implies that T and S have locally disjoint images, i.e., implies that there exists a finite band decomposition E  E D E of E such that 1 n Tf?Sf for all f 2 E and all i D 1;::: ;n. We will also study the related question whether there exists a finite band decomposition E E D E of E such that 1 n the restrictions .T C S/ are again disjointness preserving. Our approach http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Band Decompositions for Disjointness Preserving Operators

Loading next page...
 
/lp/springer_journal/band-decompositions-for-disjointness-preserving-operators-5nnuCxrWlx
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
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.
10.1023/A:1009866225070
Publisher site
See Article on Publisher Site

Abstract

Positivity 4: 259–288, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. Band Decompositions for Disjointness Preserving Operators 1 2 B. DE PAGTER and A.R. SCHEP Department of Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA 1. Introduction Let E and F be Riesz spaces with F Dedekind complete and let T;S V E ! F be order bounded linear disjointness preserving operators. The main problem we discuss in this paper is to find conditions on either T and S, or the space E,so that the property that T and S are disjoint in the space or order bounded operators from E into F , implies that T and S have locally disjoint images, i.e., implies that there exists a finite band decomposition E  E D E of E such that 1 n Tf?Sf for all f 2 E and all i D 1;::: ;n. We will also study the related question whether there exists a finite band decomposition E E D E of E such that 1 n the restrictions .T C S/ are again disjointness preserving. Our approach

Journal

PositivitySpringer Journals

Published: Oct 16, 2004

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
Access to DeepDyve database
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off