{"paper":{"title":"Orthogonally additive, orthogonality preserving, holomorphic mappings between C*-algebras","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Daniele Puglisi, Jorge J. Garc\\'es, Mar\\'ia I. Ram\\'irez","submitted_at":"2013-10-01T17:42:01Z","abstract_excerpt":"We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\\varrho) \\longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\\delta)$ and we assume that $f$ is orthogonality preserving on $A_{sa}\\cap U$, orthogonally additive on $U$ and $f(U)$ contains an invertible element in $B$, then there exist a sequence $(h_n)$ in $B^{**}$ and Jordan $^*$-homomorphisms $\\Theta, \\widetilde{\\Theta} : M(A) \\to B^{**}$ such that $$ f(x) = \\sum_{n=1}^\\infty h_n \\widetilde{\\Theta} (a^n)= \\sum_{n=1}^\\infty {\\Theta} (a^n) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0407","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"}