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.

Résumé

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.

Détail

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