{"paper":{"title":"Multiplication operators on Orlicz and weighted Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ratan Kumar Giri, Shesadev Pradhan","submitted_at":"2016-06-10T15:25:25Z","abstract_excerpt":"Let $(\\Omega,\\Sigma,\\mu)$ be a $\\sigma$-finite complete measure space, $\\tau:\\Omega\\rightarrow\\Omega$ be a measurable transformation and $\\phi$ be an Orlicz function. In this article, first a necessary and sufficient condition for the bounded multiplication operator $M_u$ on Orlicz space $L^\\phi (\\Omega)$ induced by measurable function $u$ to be completely continuous has been established. Next by using Radon-Nikodym derivative $\\omega = \\frac{d \\mu\\circ \\tau^{-1}}{d \\mu}$, the multiplication operator $M_u$ on weighted Orlicz space $L^{\\phi}_\\omega(\\Omega)$ have been characterized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03363","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"}