{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WDOQ575NEJDXJHAWEVX45USGUY","short_pith_number":"pith:WDOQ575N","schema_version":"1.0","canonical_sha256":"b0dd0effad2247749c16256fced246a622d8605568a0c7dbd3f6c5e9818a6135","source":{"kind":"arxiv","id":"1708.01475","version":1},"attestation_state":"computed","paper":{"title":"The Coburn-Simonenko theorem for Toeplitz operators acting between Hardy type subspaces of different Banach function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich","submitted_at":"2017-08-04T12:32:00Z","abstract_excerpt":"Let $\\Gamma$ be a rectifiable Jordan curve, let $X$ and $Y$ be two reflexive Banach function spaces over $\\Gamma$ such that the Cauchy singular integral operator $S$ is bounded on each of them, and let $M(X,Y)$ denote the space of pointwise multipliers from $X$ to $Y$. Consider the Riesz projection $P=(I+S)/2$, the corresponding Hardy type subspaces $PX$ and $PY$, and the Toeplitz operator $T(a):PX\\to PY$ defined by $T(a)f=P(af)$ for a symbol $a\\in M(X,Y)$. We show that if $X\\hookrightarrow Y$ and $a\\in M(X,Y)\\setminus\\{0\\}$, then $T(a)\\in\\mathcal{L}(PX,PY)$ has a trivial kernel in $PX$ or a d"},"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":"1708.01475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-04T12:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"cd8b1a24b4c5dc946fb4ba28409cb8459635e969046e0461973177aec19841ff","abstract_canon_sha256":"1639366323e3b8d0e3f370f74a2d14758a40ba85212adaa050a4b7110e4593d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:37.266587Z","signature_b64":"MINR9pnaYROaKmyCqZddfvv4ieBkNuIw7iMnAMw2a38Q7soL2Wp6EDXzZ2i/qnmxJo4OMid9D7Pms2lUhQXNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0dd0effad2247749c16256fced246a622d8605568a0c7dbd3f6c5e9818a6135","last_reissued_at":"2026-05-18T00:38:37.266097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:37.266097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Coburn-Simonenko theorem for Toeplitz operators acting between Hardy type subspaces of different Banach function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich","submitted_at":"2017-08-04T12:32:00Z","abstract_excerpt":"Let $\\Gamma$ be a rectifiable Jordan curve, let $X$ and $Y$ be two reflexive Banach function spaces over $\\Gamma$ such that the Cauchy singular integral operator $S$ is bounded on each of them, and let $M(X,Y)$ denote the space of pointwise multipliers from $X$ to $Y$. Consider the Riesz projection $P=(I+S)/2$, the corresponding Hardy type subspaces $PX$ and $PY$, and the Toeplitz operator $T(a):PX\\to PY$ defined by $T(a)f=P(af)$ for a symbol $a\\in M(X,Y)$. We show that if $X\\hookrightarrow Y$ and $a\\in M(X,Y)\\setminus\\{0\\}$, then $T(a)\\in\\mathcal{L}(PX,PY)$ has a trivial kernel in $PX$ or a d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01475","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.01475","created_at":"2026-05-18T00:38:37.266168+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.01475v1","created_at":"2026-05-18T00:38:37.266168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01475","created_at":"2026-05-18T00:38:37.266168+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDOQ575NEJDX","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDOQ575NEJDXJHAW","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDOQ575N","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY","json":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY.json","graph_json":"https://pith.science/api/pith-number/WDOQ575NEJDXJHAWEVX45USGUY/graph.json","events_json":"https://pith.science/api/pith-number/WDOQ575NEJDXJHAWEVX45USGUY/events.json","paper":"https://pith.science/paper/WDOQ575N"},"agent_actions":{"view_html":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY","download_json":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY.json","view_paper":"https://pith.science/paper/WDOQ575N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.01475&json=true","fetch_graph":"https://pith.science/api/pith-number/WDOQ575NEJDXJHAWEVX45USGUY/graph.json","fetch_events":"https://pith.science/api/pith-number/WDOQ575NEJDXJHAWEVX45USGUY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY/action/storage_attestation","attest_author":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY/action/author_attestation","sign_citation":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY/action/citation_signature","submit_replication":"https://pith.science/pith/WDOQ575NEJDXJHAWEVX45USGUY/action/replication_record"}},"created_at":"2026-05-18T00:38:37.266168+00:00","updated_at":"2026-05-18T00:38:37.266168+00:00"}