{"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. If we also assume t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07499","kind":"arxiv","version":2},"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"}