{"paper":{"title":"Module tensor product of subnormal modules need not be subnormal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akash Anand, Sameer Chavan","submitted_at":"2016-08-29T15:46:41Z","abstract_excerpt":"Let $\\kappa : \\mathbb D \\times \\mathbb D \\to \\mathbb C$ be a diagonal positive definite kernel and let $\\mathscr H_{\\kappa}$ denote the associated reproducing kernel Hilbert space of holomorphic functions on the open unit disc $\\mathbb D$. Assume that $zf \\in \\mathscr H$ whenever $f \\in \\mathscr H.$ Then $\\mathscr H$ is a Hilbert module over the polynomial ring $\\mathbb C[z]$ with module action $p \\cdot f \\mapsto pf$. We say that $\\mathscr H_{\\kappa}$ is a subnormal Hilbert module if the operator $\\mathscr M_{z}$ of multiplication by the coordinate function $z$ on $\\mathscr H_{\\kappa}$ is subn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08113","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"}