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

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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

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