{"paper":{"title":"Additivity of maps preserving Jordan $\\eta_{\\ast}$-products on $C^{*}$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ali Taghavi, Hamid Rohi, Vahid Darvish","submitted_at":"2015-04-01T04:04:44Z","abstract_excerpt":"Let $\\mathcal{A}$ and $\\mathcal{B}$ be two $C^{*}$-algebras such that $\\mathcal{B}$ is prime. In this paper, we investigate the additivity of map $\\Phi$ from $\\mathcal{A}$ onto $\\mathcal{B}$ that are bijective unital and satisfies $$\\Phi(AP+\\eta PA^{*})=\\Phi(A)\\Phi(P)+\\eta \\Phi(P)\\Phi(A)^{*},$$ for all $A\\in\\mathcal{A}$ and $P\\in\\{P_{1},I_{\\mathcal{A}}-P_{1}\\}$ where $P_{1}$ is a nontrivial projection in $\\mathcal{A}$. Let $\\eta$ be a non-zero complex number such that $|\\eta|\\neq1$, then $\\Phi$ is additive. Moreover, if $\\eta$ is rational then $\\Phi$ is $\\ast$-additive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00100","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"}