{"paper":{"title":"On a functional equation for symmetric linear operators on $C^{*}$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ali Taghavi","submitted_at":"2013-09-11T07:32:27Z","abstract_excerpt":"Let $A$ be a $C^{*}$ algebra and $T: A\\rightarrow A$ be a linear map which satisfies the functional equation $\\begin{cases}T(x)T(y)=T^{2}(xy)\\\\T(x^{*})=T(x)^{*} \\end{cases}$ We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=\\lambda x$ for some $\\lambda \\in \\mathbb{R}:$\\\\ \\begin{enumerate} \\item $A$ is a simple $C^{*}$-algebra.\n  \\item $A$ is unital with trivial center and has a faithful trace such that each zero-trace element lies in the closure of the span of commutator elements.\n  \\item $A=B(H)$ where H is a separable Hilbert space. \\end{enumerate}\n  For"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2748","kind":"arxiv","version":4},"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"}