{"paper":{"title":"Operator ideals on non-commutative function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"E. Spinu, T. Oikhberg","submitted_at":"2013-09-21T04:39:25Z","abstract_excerpt":"Suppose $X$ and $Y$ are Banach spaces, and ${\\mathcal{I}}$, ${\\mathcal{J}}$ are operator ideals (for instance, the ideals of strictly singular, weakly compact, or compact operators). Under what conditions does the inclusion ${\\mathcal{I}}(X,Y) \\subset {\\mathcal{J}}(X,Y)$, or the equality ${\\mathcal{I}}(X,Y) = {\\mathcal{J}}(X,Y)$, hold? We examine this question when ${\\mathcal{I}}, {\\mathcal{J}}$ are the ideals of Dunford-Pettis, strictly (co)singular, finitely strictly singular, inessential, or (weakly) compact operators, while $X$ and $Y$ are non-commutative function spaces. Since such spaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5434","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"}