{"paper":{"title":"Haagerup's Approximation Property and Relative Amenability","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Jon P. Bannon, Junsheng Fang","submitted_at":"2007-09-24T17:12:11Z","abstract_excerpt":"A finite von Neumann algebra $\\mathcal{M}$ with a faithful normal trace $% \\tau $ has Haagerup's approximation property (relative to a von Neumann subalgebra $\\mathcal{N}$) if there exists a net $(\\phi_{\\alpha})_{\\alpha\\in \\Lambda}$ of normal completely positive ($\\mathcal{N}$-bimodular) maps from $\\mathcal{M}$ to $\\mathcal{M}$ that satisfy the subtracial condition $% \\tau \\circ \\phi_{\\alpha}\\leq \\tau $, the extension operators $% T_{\\phi_{\\alpha}}$ are bounded compact operators (in $<\\mathcal{M%},e_{\\mathcal{N}}>$), and pointwise approximate the identity in the trace-norm, i.e., $\\lim_{\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3676","kind":"arxiv","version":4},"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"}