Geodesic
A disjointness type property of conditional expectation operators
Beata Randrianantoanina1
1 Department of Mathematics and Statistics Miami University Oxford, OH 45056, U.S.A.
Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 9-20

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator $T:X\to X$ on a Banach lattice $X$ is semi-band-preserving if and only if for all $f, g \in X$, $f \perp Tg$ implies that $Tf \perp Tg$. 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.
DOI : 10.4064/cm102-1-2
Keywords: characterization conditional expectation operators through disjointness type property similar band preserving operators say operator banach lattice semi band preserving only perp implies perp prove purely atomic banach lattice operator weighted conditional expectation operator only semi band preserving

Beata Randrianantoanina 1

1 Department of Mathematics and Statistics Miami University Oxford, OH 45056, U.S.A. 
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Beata Randrianantoanina. A disjointness type property
of conditional expectation operators. Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 9-20. doi: 10.4064/cm102-1-2

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