{"paper":{"title":"A Projection Characterization and Symmetry Bootstrap for Elements of a von Neumann Algebra that are Nearby Commuting Elements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"David Herrera","submitted_at":"2024-12-30T08:33:54Z","abstract_excerpt":"We define a symmetry map $\\varphi$ on a unital $C^\\ast$-algebra $\\mathcal A$ to be an $\\mathbb{R}$-linear map on $\\mathcal A$ that generalizes transformations on matrices like: transpose, adjoint, complex-conjugation, conjugation by a unitary matrix, and their compositions. We include an overview of such symmetry maps on unital $C^\\ast$-algebras. We say that $A\\in\\mathcal A$ is $\\varphi$-symmetric if $\\varphi(A)=A$, $A$ is $\\varphi$-antisymmetric if $\\varphi(A)=-A$, and $A$ has a $\\zeta=e^{i\\theta}$ $\\varphi$-phase symmetry if $\\varphi(A)=\\zeta A$.\n  Our main result is a new projection charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20795","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20795/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}