{"paper":{"title":"Factorizations of Characteristic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Amit Maji, Jaydeb Sarkar, Kalpesh J. Haria","submitted_at":"2016-04-17T10:25:56Z","abstract_excerpt":"Let $A = (A_1, \\ldots, A_n)$ and $B = (B_1, \\ldots, B_n)$ be row contractions on $\\mathcal{H}_1$ and $\\mathcal{H}_2$, respectively, and $X$ be a row operator from $\\oplus_{i=1}^n \\mathcal{H}_2$ to $\\mathcal{H}_1$. Let $D_{A^*} = (I - A A^*)^{\\frac{1}{2}}$ and $D_{B} = (I - B^* B)^{\\frac{1}{2}}$ and $\\Theta_T$ be the characteristic function of $T = \\begin{bmatrix} A& D_{A^*}L D_B\\\\ 0 & B \\end{bmatrix}$. Then $\\Theta_T$ coincides with the product of the characteristic function $\\Theta_A$ of $A$, the Julia-Halmos matrix corresponding to $L$ and the characteristic function $\\Theta_B$ of $B$. More "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04858","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"}