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## A disjointness type property of conditional expectation operators

### Tom 102 / 2005

Colloquium Mathematicum 102 (2005), 9-20 MSC: 46B42, 46B45. DOI: 10.4064/cm102-1-2

#### Streszczenie

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.

#### Autorzy

• Beata RandrianantoaninaDepartment of Mathematics and Statistics
Miami University
Oxford, OH 45056, U.S.A.
e-mail

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