{"paper":{"title":"Multiplication operators on vector-valued function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arkady Kitover, Hulya Duru, Mehmet Orhon","submitted_at":"2011-04-14T15:40:19Z","abstract_excerpt":"Let $E$ be a Banach function space on a probability measure space $(\\Omega ,\\Sigma,\\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\\\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is given by multiplication by a function in $L^{\\infty}(\\mu).$ In the main result of this paper, we show that an operator $T$ on $E(X)$ is a multiplication operator if and only if $T$ commutes with $L^{\\infty}(\\mu)$ and leaves invariant the cyclic subspaces generated by the constant vector-valued functions in $E(X).$ As a corollary we show that this is equivalent "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2806","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"}