{"paper":{"title":"Orthogonally additive and orthogonally multiplicative holomorphic functions of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Chingjou Liao, Ngai-Ching Wong, Qingying Bu","submitted_at":"2014-02-27T10:20:10Z","abstract_excerpt":"Let $H:M_m\\to M_m$ be a holomorphic function of the algebra $M_m$ of complex $m\\times m$ matrices. Suppose that $H$ is orthogonally additive and orthogonally multiplicative on self-adjoint elements. We show that either the range of $H$ consists of zero trace elements, or there is a scalar sequence $\\{\\lambda_n\\}$ and an invertible $S$ in $M_m$ such that $$ H(x) =\\sum_{n\\geq 1} \\lambda_n S^{-1}x^nS, \\quad\\forall x \\in M_m,%\\eqno{(\\ddag)} $$ or $$ H(x) =\\sum_{n\\geq 1} \\lambda_n S^{-1}(x^t)^nS, \\quad\\forall x \\in M_m. $$ Here, $x^t$ is the transpose of the matrix $x$. In the latter case, we alway"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6849","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"}