  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.
