{"paper":{"title":"Universal Non-Completely-Continuous Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Maria Girardi, William B. Johnson","submitted_at":"1995-04-13T15:44:32Z","abstract_excerpt":"A bounded linear operator between Banach spaces is called {\\it completely continuous} if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from $L_1$ into an arbitrary Banach space, namely, the operator from $L_1$ into $\\ell_\\infty$ defined by $$ T_0 (f) =\\left( \\int r_n f \\, d\\mu \\right)_{n\\ge 0} \\ , $$ where $r_n$ is the $n^{\\text{th}}$ Rademacher function. It is also shown that there does not exist a universal operator for the class of non-completely-continuous operators between two ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9504205","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"}