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We show that the lattice of closed ideals of~$\\mathscr{B}(X)$ has a very rich structure; in particular $\\mathscr{B}(X)$ contains at least continuum many maximal ideals.\n  Our approach is to study the closed ideals generated by the basis projections. Indeed, the unit vector basis is an unconditional basis for each of the above spaces, so there is a basis projection $P_N\\in\\mathscr{B}(X)$ corresponding to each non-em"},"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":"1907.10645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-24T18:15:41Z","cross_cats_sorted":[],"title_canon_sha256":"824d4ad69d26a1f44f37f4553d6554823b9c3c630547202d745cd43f9ced54fa","abstract_canon_sha256":"9495ab2b5199f86fe3bc382749397e164f17310deb752e23ada9c95271ffdeec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:29.848652Z","signature_b64":"xq1cNwv3ybTYcTWUYVcVprPxHhAltYqJXtEUmBDzWVEA7OI3zbgVOqOcxlnPXncZSh37oQnYL3PJ1qWM9JjEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b39a718f95b9b2a4effdd9fe2dc29043832d234f9e4134bd044c632f3ac8096","last_reissued_at":"2026-07-05T00:54:29.848282Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:29.848282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed ideals of operators on the Tsirelson and Schreier spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Beanland, Niels Jakob Laustsen, Tomasz Kania","submitted_at":"2019-07-24T18:15:41Z","abstract_excerpt":"Let $\\mathscr{B}(X)$ denote the Banach algebra of bounded operators on $X$, where~$X$ is either Tsirelson's Banach space or the Schreier space of order $n$ for some $n\\in\\mathbb N$. 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