{"paper":{"title":"Unbounded Operators on Hilbert $C^*$-Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Konrad Schm\\\"udgen, Ren\\'e Gebhardt","submitted_at":"2014-09-30T12:43:01Z","abstract_excerpt":"Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\\to F$ are introduced and investigated. Instead of the density of the domain $\\Def(t)$ we only assume that $t$ is essentially defined, that is, $\\Def(t)^\\bot=\\{0\\}$. Then $t$ has a well-defined adjoint. We call an essentially defined operator $t$ graph regular if its graph $\\Graph(t)$ is orthogonally complemented in $E\\oplus F$ and orthogonally closed if $\\Graph(t)^{\\bot\\bot}=\\Graph(t)$. A theory of these operators is developed. Various characterizations of graph regular "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8523","kind":"arxiv","version":2},"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"}