{"paper":{"title":"Schur-Horn theorems in II$_\\infty$-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Martin Argerami, Pedro Massey","submitted_at":"2011-05-30T23:55:00Z","abstract_excerpt":"We describe majorization between selfadjoint operators in a $\\sigma$-finite II$_\\infty$ factor $(\\mathcal{M},\\tau)$ in terms of simple spectral relations. For a diffuse abelian von Neumann subalgebra $\\mathcal{A}\\subset \\mathcal{M}$ with trace-preserving conditional expectation $E_{\\mathcal{A}}$, we characterize the closure in the measure topology of the image through $E_{\\mathcal{A}}$ of the unitary orbit of a selfadjoint operator in $\\mathcal{M}$ in terms of majorization (i.e., a Schur-Horn theorem). We also obtain similar results for the contractive orbit of positive operators in $\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6140","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"}