{"paper":{"title":"The Schur-Horn theorem for operators with finite spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"B. V. Rajarama Bhat, Mohan Ravichandran","submitted_at":"2011-11-16T15:25:19Z","abstract_excerpt":"The carpenter problem in the context of $II_1$ factors, formulated by Kadison asks: Let $\\mathcal{A} \\subset \\mathcal{M}$ be a masa in a type $II_1$ factor and let $E$ be the normal conditional expectation from $\\mathcal{M}$ onto $\\mathcal{A}$. Then, is it true that for every positive contraction $A$ in $\\mathcal{A}$, there is a projection $P$ in $\\mathcal{M}$ such that $E(P) = A$? In this note, we show that this is true if $A$ has finite spectrum. We will then use this result to prove an exact Schur-Horn theorem for (positive)operators with finite spectrum and an approximate Schur-Horn theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3833","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"}