{"paper":{"title":"Matricial Function Theory and Weighted Shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Baruch Solel, Paul S. Muhly","submitted_at":"2015-07-08T12:04:50Z","abstract_excerpt":"Let $\\mathcal{T}_{+}(E)$ be the tensor algebra of a $W^{*}$-correspondence $E$ over a $W^{*}$-algebra $M$. In earlier work, we showed that the completely contractive representations of $\\mathcal{T}_{+}(E)$, whose restrictions to $M$ are normal, are parametrized by certain discs or balls $\\overline{D(E,\\sigma)}$ indexed by the normal $*$-representations $\\sigma$ of $M$. Each disc has analytic structure, and each element $F\\in \\mathcal{T}_{+}(E) $ gives rise to an operator-valued function $\\widehat{F}_{\\sigma}$ on $\\overline{D(E,\\sigma)}$ that is continuous and analytic on the interior. In this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02115","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"}