{"paper":{"title":"On the optimal paving over MASAs in von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sorin Popa, Stefaan Vaes","submitted_at":"2015-07-04T05:50:52Z","abstract_excerpt":"We prove that if $A$ is a singular MASA in a II$_1$ factor $M$ and $\\omega$ is a free ultrafilter, then for any $x\\in M\\ominus A$, with $\\|x\\|\\leq 1$, and any $n\\geq 2$, there exists a partition of $1$ with projections $p_1, p_2, ..., p_n\\in A^\\omega$ (i.e. a {\\it paving}) such that $\\|\\Sigma_{i=1}^n p_i x p_i\\|\\leq 2\\sqrt{n-1}/n$, and give examples where this is sharp. Some open problems on optimal pavings are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01072","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"}