{"paper":{"title":"A disjointness type property of conditional expectation operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Beata Randrianantoanina","submitted_at":"2001-12-18T17:13:40Z","abstract_excerpt":"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\n $X$ 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0112181","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}