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We determine generators of these algebras and consider a Riesz type factorization theorem for the non-commutative $H^1$ space. We show that the right analytic Toeplitz algebra on the non-commutative Hardy space $H^p$ associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive."},"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":"1904.01746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-04-03T03:07:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8075c9afeaad7e164d2dd9e774ffd3ee997818f4f626a2ac32e95907576a5f8f","abstract_canon_sha256":"e89473d91df82b5bd303b7cdd6b75cdcc2f1bcc752715f61b728382de09d151d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:29.823578Z","signature_b64":"dQRBA5aQbo3CHX1JUEjTj9j0yG89sPlLbAJfLh8gfvBNvgy59dn9H6MEzEFISitslE8sQwMiN+Ayx6bLZ6LkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5378b531e1705146e0972b290539989533e8a6ccc47db8315aa540195cb60a10","last_reissued_at":"2026-05-17T23:49:29.822960Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:29.822960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subdiagonal algebras with the Beurling type invariant subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Guoxing Ji","submitted_at":"2019-04-03T03:07:23Z","abstract_excerpt":"Let $\\mathfrak A$ be a maximal subdiagonal algebra in a $\\sigma$-finite von Neumann algebra $\\mathcal M$. 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