{"paper":{"title":"Hilbert space operators with compatible off-diagonal corners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. MacDonald, H. Radjavi, L. Livshits, L.W. Marcoux","submitted_at":"2017-09-06T14:36:28Z","abstract_excerpt":"Given a complex, separable Hilbert space $\\mathcal{H}$, we characterize those operators for which $\\| P T (I-P) \\| = \\| (I-P) T P \\|$ for all orthogonal projections $P$ on $\\mathcal{H}$. When $\\mathcal{H}$ is finite-dimensional, we also obtain a complete characterization of those operators for which $\\mathrm{rank}\\, (I-P) T P = \\mathrm{rank}\\, P T (I-P)$ for all orthogonal projections $P$. When $\\mathcal{H}$ is infinite-dimensional, we show that any operator with the latter property is normal, and its spectrum is contained in either a line or a circle in the complex plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01840","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"}