{"paper":{"title":"Pointwise products of some Banach function spaces and factorization","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Karol Le\\'snik, Lech Maligranda, Pawe{\\l} Kolwicz","submitted_at":"2012-11-13T21:18:11Z","abstract_excerpt":"The well-known factorization theorem of Lozanovski{\\u \\i} may be written in the form $L^{1}\\equiv E\\odot E^{\\prime}$, where $\\odot $ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the question when one can factorize $F$ through $E$, i.e., when $F\\equiv E\\odot M(E, F) \\,$, where $M(E, F) $ is the space of pointwise multipliers from $E$ to $F$. Properties of $M(E, F) $ were investigated in our earlier paper [KLM12] and here we collect and prove some properties of the construction $E\\odot F$. The formulas for pointwise product of Calder\\'{o}n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3135","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"}