{"paper":{"title":"Linear maps between C*-algebras that are *-homomorphisms at a fixed point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, J. Cabello-S\\'anchez, Mar\\'ia J. Burgos","submitted_at":"2016-09-25T17:40:31Z","abstract_excerpt":"Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\\to B$ is said to be a $^*$-homomorphism at an element $z\\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$ Assuming that $A$ is unital, we prove that every linear map $T: A\\to B$ which is a $^*$-homomorphism at the unit of $A$ is a Jordan $^*$-homomorphism. If $A$ is simple and infinite, then we establish that a linear map $T: A\\to B$ is a $^*$-homomorphism if and only if $T$ is a $^*$-homomorphism at the unit of $A$. For a general unital C$^*$-algebra $A$ and a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07776","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"}