{"paper":{"title":"Maps preserving peripheral spectrum of generalized Jordan products of operators","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Jinchuan Hou, Wen Zhang, Xiaofei Qi","submitted_at":"2014-02-05T06:20:21Z","abstract_excerpt":"Let $X_1$ and $X_2$ be complex Banach spaces with dimension at least three, $\\mathcal{A}_1$ and $\\mathcal{A}_2$ be standard operator algebras on $X_1$ and $X_2$, respectively. For $k\\geq2$, let $(i_1,...,i_m)$ be a sequence with terms chosen from $\\{1,\\ldots,k\\}$ and assume that at least one of the terms in $(i_1,\\ldots,i_m)$ appears exactly once. Define the generalized Jordan product $T_1\\circ T_2\\circ\\cdots\\circ T_k=T_{i_1} T_{i_2}\\cdots T_{i_m}+T_{i_m}\\cdots T_{i_2} T_{i_1}$ on elements in $\\mathcal{A}_i$. This includes the usual Jordan product $A_1A_2+A_2A_1$, and the Jordan triple $A_1A_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0946","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"}