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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.5434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-21T04:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"ac64fb532acd8cc8a46a26ff56d7b6e7cb61313b72ca120590de47b9291bb21f","abstract_canon_sha256":"566bcff52fed110d6007ce05168b59fe1bfeaf0e266fadb29992e7163c10a5e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:45.681961Z","signature_b64":"NXHdyGBqgiN7wNAB50zPK3fj0NT5iFa3pNZhTOxztGDfRpS66kr9FoaL5fv5NIYAiNFGqXAlnzAxe8kH/bSWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a6f3362a9a4d1c7dbd6b7f3367f7ae6964ffae8c349287ea6a0d4a504a5d9d9","last_reissued_at":"2026-05-18T03:12:45.681349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:45.681349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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