{"paper":{"title":"Factorization in weak products of complete Pick spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael T. Jury, Robert T.W. Martin","submitted_at":"2018-06-13T21:16:39Z","abstract_excerpt":"Let $\\mathcal H$ be a reproducing kernel Hilbert space with a normalized complete Nevanlinna-Pick (CNP) kernel. We prove that if $(f_n)$ is a sequence of functions in $\\mathcal H$ with $\\sum\\|f_n\\|^2<\\infty$, then there exists a contractive column multiplier $(\\varphi_n)$ of $\\mathcal H$ and a cyclic vector $F\\in \\mathcal H$ so that $\\varphi_ n F=f_n$ for all $n$.\n  The space of weak products $\\mathcal H\\odot\\mathcal H$ is the set of functions of the form $h=\\sum_{i=1}^\\infty f_ig_i$ with $f_i, g_i\\in\\mathcal H$ and $\\sum_{i=1}^\\infty \\|f_i\\|\\|g_i\\|<\\infty$. Using the above result, in combinat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05268","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"}