{"paper":{"title":"Extension of order bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kazem Haghnejad Azar","submitted_at":"2019-05-26T03:43:16Z","abstract_excerpt":"Assume that a normed lattice $E$ is order dense majorizing of a vector lattice $E^t$. There is an extension norm $\\Vert.\\Vert_t$ for $E^t$ and we extend some lattice and topological properties of normed lattice $(E,\\Vert.\\Vert)$ to new normed lattice $(E^t,\\Vert.\\Vert_t$). For a Dedekind complete Banach lattice $F$, $T^t$ is an extension of $T$ from $E^t$ into $F$ whenever $T$ is an order bounded operator from $E$ into $F$. For each positive operator $T$, we have $\\Vert T\\Vert=\\Vert T^t\\Vert$ and we show that $T^t$ is a lattice homomorphism from $E^t$ into $F$ and moreover $T^t\\in \\mathcal{L}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10721","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"}