{"paper":{"title":"A Maurey type result for operator spaces","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Hun Hee Lee, Marius Junge","submitted_at":"2007-07-02T06:34:13Z","abstract_excerpt":"The little Grothendieck theorem for Banach spaces says that every bounded linear operator between $C(K)$ and $\\ell_2$ is 2-summing. However, it is shown in \\cite{J05} that the operator space analogue fails. Not every cb-map $v : \\K \\to OH$ is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem : Every cb-map $v : \\K \\to OH$ is $(q,cb)$-summing for any $q>2$ and hence admits a factorization $\\|v(x)\\| \\leq c(q) \\|v\\|_{cb} \\|axb\\|_q$ with $a,b$ in the unit ball of the Schatten class $S_{2q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0152","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0707.0152/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}