{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:B7455CZGKPW562YNNX55FEJ4J2","short_pith_number":"pith:B7455CZG","schema_version":"1.0","canonical_sha256":"0ff9de8b2653eddf6b0d6dfbd2913c4eaa8a22e8b31829d6ada901382a9bd812","source":{"kind":"arxiv","id":"1509.08356","version":1},"attestation_state":"computed","paper":{"title":"Strict singularity of a Volterra-type integral operator on $H^p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Santeri Miihkinen","submitted_at":"2015-09-28T15:23:15Z","abstract_excerpt":"We prove that a Volterra-type integral operator $T_gf(z) = \\int_0^z f(\\zeta)g'(\\zeta)d\\zeta, \\, z \\in \\mathbb D,$ defined on Hardy spaces $H^p, \\, 1 \\le p < \\infty,$ fixes an isomorphic copy of $\\ell^p,$ if the operator $T_g$ is not compact. In particular, this shows that the strict singularity of the operator $T_g$ coincides with the compactness of the operator $T_g$ on spaces $H^p.$ As a consequence, we obtain a new proof for the equivalence of the compactness and the weak compactness of the operator $T_g$ on $H^1$."},"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":"1509.08356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-28T15:23:15Z","cross_cats_sorted":[],"title_canon_sha256":"f4b9f58d581abcccf31071f149f09b8d96694e2797a61ea5c3a04127b50cc10d","abstract_canon_sha256":"83d745741b0ca9e10c3583863beda5ea016f979f2acfaf780aa114840be2dac1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:54.093009Z","signature_b64":"WKLqqg8l0VuDqYhOisnaJk7XJcsl3UOg3OAKZA0hEOtcpL63hq/9Ro4t7S5U1w715LUpRBzT+y+9musOdJO1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff9de8b2653eddf6b0d6dfbd2913c4eaa8a22e8b31829d6ada901382a9bd812","last_reissued_at":"2026-05-18T01:31:54.092346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:54.092346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strict singularity of a Volterra-type integral operator on $H^p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Santeri Miihkinen","submitted_at":"2015-09-28T15:23:15Z","abstract_excerpt":"We prove that a Volterra-type integral operator $T_gf(z) = \\int_0^z f(\\zeta)g'(\\zeta)d\\zeta, \\, z \\in \\mathbb D,$ defined on Hardy spaces $H^p, \\, 1 \\le p < \\infty,$ fixes an isomorphic copy of $\\ell^p,$ if the operator $T_g$ is not compact. In particular, this shows that the strict singularity of the operator $T_g$ coincides with the compactness of the operator $T_g$ on spaces $H^p.$ As a consequence, we obtain a new proof for the equivalence of the compactness and the weak compactness of the operator $T_g$ on $H^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08356","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":"1509.08356","created_at":"2026-05-18T01:31:54.092453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08356v1","created_at":"2026-05-18T01:31:54.092453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08356","created_at":"2026-05-18T01:31:54.092453+00:00"},{"alias_kind":"pith_short_12","alias_value":"B7455CZGKPW5","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B7455CZGKPW562YN","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B7455CZG","created_at":"2026-05-18T12:29:14.074870+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/B7455CZGKPW562YNNX55FEJ4J2","json":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2.json","graph_json":"https://pith.science/api/pith-number/B7455CZGKPW562YNNX55FEJ4J2/graph.json","events_json":"https://pith.science/api/pith-number/B7455CZGKPW562YNNX55FEJ4J2/events.json","paper":"https://pith.science/paper/B7455CZG"},"agent_actions":{"view_html":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2","download_json":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2.json","view_paper":"https://pith.science/paper/B7455CZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08356&json=true","fetch_graph":"https://pith.science/api/pith-number/B7455CZGKPW562YNNX55FEJ4J2/graph.json","fetch_events":"https://pith.science/api/pith-number/B7455CZGKPW562YNNX55FEJ4J2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2/action/storage_attestation","attest_author":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2/action/author_attestation","sign_citation":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2/action/citation_signature","submit_replication":"https://pith.science/pith/B7455CZGKPW562YNNX55FEJ4J2/action/replication_record"}},"created_at":"2026-05-18T01:31:54.092453+00:00","updated_at":"2026-05-18T01:31:54.092453+00:00"}