{"paper":{"title":"A local quantization principle for inclusions of tracial von Neumann algebras","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Chunlan Jiang, Junsheng Fang, Xinyan Cao, Zhaolin Yao","submitted_at":"2025-07-06T05:07:14Z","abstract_excerpt":"We study the local quantization principle (after Sorin Popa~\\cite{popa 94} and \\cite{popa 95}) of inclusions of tracial von Neumann algebras. Let $(\\mathcal{M},\\tau)$ be a type ${\\rm II}_1$ von Neumann algebra and let $\\mathcal{N}\\subseteq \\mathcal{M}$ be a type ${\\rm II}_1$ von Neumann subalgebra. Let $x_1,\\ldots, x_m \\in \\mathcal{M}$ and $ \\epsilon> 0$. Then there exists a partition of 1 with projections $p_{1}, \\ldots, p_{n}$ in $\\mathcal{N}$ such that \\[\\left\\|\\sum_{i=1}^n p_{i}\\left(x_j-E_{\\mathcal{N}'\\cap \\mathcal{M}}(x_j)\\right)p_{i}\\right\\|_{2}<\\epsilon,\\quad 1\\leq j\\leq m.\\] In partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04244","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/2507.04244/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"}