{"paper":{"title":"Theory of Amalgamated Lp Spaces in Noncommutative Probability","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Javier Parcet, Marius Junge","submitted_at":"2005-11-16T10:19:23Z","abstract_excerpt":"Let $f_1, f_2, ..., f_n$ be a family of independent copies of a given random variable f in a probability space $(\\Omega, \\mathcal{F}, \\mu)$. Then, the following equivalence of norms holds whenever $1 \\le q \\le p < \\infty$ $$\\Big(\\int_{\\Omega} \\Big[ \\sum_{k=1}^n |f_k|^q \\Big]^{\\frac{p}{q}} d \\mu \\Big)^{\\frac1p} \\sim \\max_{r \\in \\{p,q\\}} {n^{\\frac1r} \\Big(\\int_\\Omega |f|^r d\\mu \\Big)^{\\frac1r}}.$$ We prove a noncommutative analogue of this inequality for sums of free random variables over a given von Neumann subalgebra. This formulation leads to new classes of noncommutative function spaces whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511406","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/math/0511406/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"}