2001/12/18 by Beata Randrianantoanina, Randrianantoanina, Beata
Computer Science · Mathematics · #46B42 #46B45 #Advanced Algebra and Logic #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.math/0112181
openalex publication_date 2001/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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→ X on a Banach lattice X is semi band preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ 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.