{"paper":{"title":"Spaceability in sets of operators on $C(K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Leonardo Pellegrini, Pedro Kaufmann, Rog\\'erio Fajardo","submitted_at":"2012-03-30T16:50:24Z","abstract_excerpt":"We show that when $C(K)$ does not have few operator -- in the sense of Koszmider [P. Koszmider, Banach spaces of continuous functions with few operators. Math. Ann. 300 (2004), no. 1, 151 - 183.] -- the sets of operators which are not weak multipliers is spaceable. This shows a contrast with what happens in general Banach spaces that do not have few operators.\n  In addition, we show that there exist a $C(K)$ space such that each operator on it is of the form $gI+hJ+S$, where $g,h\\in C(K)$ and $S$ is strictly singular, in connection to a result by Ferenczi [V. Ferenczi,Uniqueness of complex str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6855","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":""},"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"}