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We prove that every bijective map $\\Phi:M\\to N$ satisfying $$\\Phi(\\Delta_{\\lambda}(a\\circ b^*))=\\Delta_{\\lambda}(\\Phi(a) \\circ \\Phi(b)^*), \\hbox{ for all } a,\\;b\\in M,$$ (for a fixed $\\lambda\\in [0,1]$), maps the hermitian part of $M$ onto the hermitian part of $N$ (i.e. $\\Phi (M_{sa}) = N_{sa}$) and its restriction $\\Phi|_{M_{sa}} : M_{sa}\\to N_{sa}$ is a Jordan isomorphism. If we also assume t"},"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":"1712.07499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-20T14:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"ad1b78d74db86237a6714192d9801a7304fec60adadddc1fbc0b2e7250f55743","abstract_canon_sha256":"1fb238c071f691e034ebc786ae0288eb85a83d42fe39c1cd220d19cd4455beb2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:24.314711Z","signature_b64":"qeZBGgs1ROr/sk2+kkP4Gs+Zh72eeRstOGNzY4rW7IVCJEMWU4bUWW76iH6dEOpIww1bCdSesxdpY747rCl6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e809bd36ad401508c6703fab290bf57de90fba8810548f7f9636a647c8da37e","last_reissued_at":"2026-05-18T00:27:24.314140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:24.314140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Preservers of $\\lambda$-Aluthge transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ahlem Ben Ali Essaleh, Antonio M. Peralta","submitted_at":"2017-12-20T14:43:49Z","abstract_excerpt":"Let $M$ and $N$ be arbitrary von Neumann algebras. For any $a$ in $M$ or in $N$, let $\\Delta_{\\lambda}(a)$ denote the $\\lambda$-Aluthge transform of $a$. Suppose that $M$ has no abelian direct summand. We prove that every bijective map $\\Phi:M\\to N$ satisfying $$\\Phi(\\Delta_{\\lambda}(a\\circ b^*))=\\Delta_{\\lambda}(\\Phi(a) \\circ \\Phi(b)^*), \\hbox{ for all } a,\\;b\\in M,$$ (for a fixed $\\lambda\\in [0,1]$), maps the hermitian part of $M$ onto the hermitian part of $N$ (i.e. $\\Phi (M_{sa}) = N_{sa}$) and its restriction $\\Phi|_{M_{sa}} : M_{sa}\\to N_{sa}$ is a Jordan isomorphism. 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