{"paper":{"title":"Orthogonally $a$-Jensen mappings on $C^*$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Ali Zamani","submitted_at":"2018-11-17T12:02:47Z","abstract_excerpt":"We investigate the representation of the so-called orthogonally $a$-Jensen mappings acting on $C^*$-modules. More precisely, let $\\mathfrak{A}$ be a unital $C^*$-algebra with the unit $1$, let $a \\in \\mathfrak{A}$ be fixed such that $a, 1-a$ are invertible and let $\\mathscr{E}, \\mathscr{F}, \\mathscr{G}$ be inner product $\\mathfrak{A}$-modules. We prove that if there exist additive mappings $\\varphi, \\psi$ from $\\mathscr{F}$ into $\\mathscr{E}$ such that $\\big\\langle \\varphi(y), \\psi(z)\\big\\rangle=0$ and $a \\big\\langle \\varphi(y), \\varphi(z)\\big\\rangle a^\\ast = (1 - a)\\big\\langle \\psi(y), \\psi(z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07148","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"}