A characterization of positively decomposable non-linear maps between Banach lattices

A characterization of positively decomposable non-linear maps between Banach lattices A map between Banach lattices E and F is called positively decomposable if Tf = g 1 + g 2 for f, g 1, g 2 positive and g 1 and g 2 disjoint implies there exist disjoint positive elements f 1 and f 2 each less than f with the property that Tf 1 = g 1 and Tf 2 = g 2. Recently, the positive decomposability of linear Carleman operators on Banach lattices were characterized using disjointness condition of images of the approximate atoms. This note provides an extension of the characterization for a class of non-linear maps. Further, disjointness preserving maps are studied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A characterization of positively decomposable non-linear maps between Banach lattices

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science + Business Media B.V.
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2115-5
Publisher site
See Article on Publisher Site

Abstract

A map between Banach lattices E and F is called positively decomposable if Tf = g 1 + g 2 for f, g 1, g 2 positive and g 1 and g 2 disjoint implies there exist disjoint positive elements f 1 and f 2 each less than f with the property that Tf 1 = g 1 and Tf 2 = g 2. Recently, the positive decomposability of linear Carleman operators on Banach lattices were characterized using disjointness condition of images of the approximate atoms. This note provides an extension of the characterization for a class of non-linear maps. Further, disjointness preserving maps are studied.

Journal

PositivitySpringer Journals

Published: Jul 16, 2008

References

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