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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.0946","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2014-02-05T06:20:21Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"6d8ace5fbae268ec94dfcbf3ede3cc697e70cf3b9736ac87b969f5cd87b81f05","abstract_canon_sha256":"1475580dd82ac5a4834169040aba414578f373b65ae5bf7ba7005919774b74fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:02.222782Z","signature_b64":"WEcozDSjnqqlutBRElVNntv3oIr6wcMZ/D68ci2hTY7MKT5VZy2KTNmLsQ3EngyBByCpsmZPX2dTYUw16pbTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a6cd577fd864d3f7559ec9bb32ad0433e3823d92471fe0230ac5b1330601e43","last_reissued_at":"2026-05-18T03:00:02.222212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:02.222212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathcal{A}_i$. 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