{"paper":{"title":"Factoring a quadratic operator as a product of two positive contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chi-Kwong Li, Ming-Cheng Tsai","submitted_at":"2014-05-16T01:11:10Z","abstract_excerpt":"Let $T$ be a quadratic operator on a complex Hilbert space $H$. We show that $T$ can be written as a product of two positive contractions if and only if $T$ is of the form $$aI \\oplus bI \\oplus\\begin{pmatrix} aI & P \\cr 0 & bI \\cr \\end{pmatrix} \\quad \\text{on} \\quad H_1\\oplus H_2\\oplus (H_3\\oplus H_3)$$ for some $a, b\\in [0,1]$ and strictly positive operator $P$ with $\\|P\\| \\le |\\sqrt{a} - \\sqrt{b}|\\sqrt{(1-a)(1-b)}.$ Also, we give a necessary condition for a bounded linear operator $T$ with operator matrix $\\begin{pmatrix} T_1 & T_3\\\\ 0 & T_2\\cr\\end{pmatrix}$ on $H\\oplus K$ that can be writte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4042","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"}