{"paper":{"title":"Characterization of Riesz spaces with topologically full center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"\\c{S}afak Alpay, Mehmet Orhon","submitted_at":"2014-06-24T19:00:51Z","abstract_excerpt":"Let $E$ be a Riesz space and let $E^{\\sim}$ denote its order dual. The orthomorphisms $Orth(E)$ on $E,$ and the ideal center $Z(E)$ of $E,$ are naturally embedded in $Orth(E^{\\sim})$ and $Z(E^{\\sim})$ respectively. We construct two unital algebra and order continuous Riesz homomorphisms \\[ \\gamma:((Orth(E))^{\\sim})_{n}^{\\sim}\\rightarrow Orth(E^{\\sim})\\text{ }% \\] and \\[ m:Z(E)^{\\prime\\prime}\\rightarrow Z(E^{\\sim}) \\] that extend the above mentioned natural inclusions respectively. Then, the range of $\\gamma$ is an order ideal in $Orth(E^{\\sim})$ if and only if $m$ is surjective. Furthermore, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6335","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"}