{"paper":{"title":"Sums of compositions of pairs of projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adam Paszkiewicz, Andrzej Komisarski","submitted_at":"2014-06-13T12:47:36Z","abstract_excerpt":"We give some necessary and sufficient conditions for the possibility to represent a Hermitian operator on an infinite-dimensional Hilbert space (real or complex) in the form $\\sum_{i=1}^nQ_iP_i$, where $P_1,\\dots,P_n$, $Q_1,\\dots,Q_n$ are orthogonal projections. We show that the smallest number $n=n(c)$ admitting the representation $x=\\sum_{i=1}^{n(c)}Q_iP_i$ for every $x=x^*$ with $\\|x\\|\\leq c$ satisfies $8c+\\frac83\\leq n(c)\\leq 8c+10$. This is a partial answer to the question asked by L. W. Marcoux in 2010."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3522","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"}