A disjointness type property of conditional expectation operators

Tom 102 / 2005

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


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.


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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek