{"paper":{"title":"Normal operators with highly incompatible off-diagonal corners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Heydar Radjavi, Laurent W. Marcoux, Yuanhang Zhang","submitted_at":"2019-08-19T18:57:16Z","abstract_excerpt":"Let $\\mathcal{H}$ be a complex, separable Hilbert space, and $\\mathcal{B}(\\mathcal{H})$ denote the set of all bounded linear operators on $\\mathcal{H}$. Given an orthogonal projection $P \\in \\mathcal{B}(\\mathcal{H})$ and an operator $D \\in \\mathcal{B}(\\mathcal{H})$, we may write $D=\\begin{bmatrix} D_1& D_2 D_3 & D_4 \\end{bmatrix}$ relative to the decomposition $\\mathcal{H} = \\mathrm{ran}\\, P \\oplus \\mathrm{ran}\\, (I-P)$. In this paper we study the question: for which non-negative integers $j, k$ can we find a normal operator $D$ and an orthogonal projection $P$ such that $\\mathrm{rank}\\, D_2 ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07024","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/1908.07024/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"}