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.
Positivity – Springer Journals
Published: Jul 16, 2008
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