{"paper":{"title":"Factorizations of Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"B. Krishna Das, Jaydeb Sarkar, Srijan Sarkar","submitted_at":"2016-07-20T04:13:57Z","abstract_excerpt":"The celebrated theorem of Berger, Coburn and Lebow on pairs of commuting isometries can be formulated as follows: a pure isometry $V$ on a Hilbert space $\\mathcal{H}$ is a product of two commuting isometries $V_1$ and $V_2$ in $\\mathcal{B}(\\mathcal{H})$ if and only if there exists a Hilbert space $\\mathcal{E}$, a unitary $U$ in $\\mathcal{B}(\\mathcal{E})$ and an orthogonal projection $P$ in $\\mathcal{B}(\\mathcal{E})$ such that $(V, V_1, V_2)$ and $(M_z, M_{\\Phi}, M_{\\Psi})$ on $H^2_{\\mathcal{E}}(\\mathbb{D})$ are unitarily equivalent, where \\[ \\Phi(z)=(P+zP^{\\perp})U^*\\;\\text{and}\\; \\Psi(z)=U(P^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05815","kind":"arxiv","version":3},"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"}