{"paper":{"title":"Tensorial Function Theory: From Berezin transforms to Taylor's Taylor series and back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA","math.RA"],"primary_cat":"math.OA","authors_text":"Baruch Solel, Paul S. Muhly","submitted_at":"2012-10-10T16:03:26Z","abstract_excerpt":"Let $H^{\\infty}(E)$ be the Hardy algebra of a $W^{*}$-correspondence $E$ over a $W^{*}$-algebra $M$. Then the ultraweakly continuous completely contractive representations of $H^{\\infty}(E)$ are parametrized by certain sets $\\mathcal{AC}(\\sigma)$ indexed by $NRep(M)$ - the normal *-representations $\\sigma$ of $M$. Each set $\\mathcal{AC}(\\sigma)$ has analytic structure, and each element $F\\in H^{\\infty}(E)$ gives rise to an analytic operator-valued function $\\hat{F}_{\\sigma}$ on $\\mathcal{AC}(\\sigma)$ that we call the $\\sigma$-Berezin transform of $F$. The sets ${\\mathcal{AC}(\\sigma)}_{\\sigma\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2964","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"}