We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-2,
author = {Beata Randrianantoanina},
title = {A disjointness type property of conditional expectation operators},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {9-20},
zbl = {1080.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-2}
}
Beata Randrianantoanina. A disjointness type property of conditional expectation operators. Colloquium Mathematicae, Tome 103 (2005) pp. 9-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-2/