{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3ZEOGDI6TEM7QK5EPMFAVIKQR6","short_pith_number":"pith:3ZEOGDI6","schema_version":"1.0","canonical_sha256":"de48e30d1e9919f82ba47b0a0aa1508f89cc8c94cf24c160ebf47bdbc96d892e","source":{"kind":"arxiv","id":"1706.03638","version":1},"attestation_state":"computed","paper":{"title":"Ces\\`aro bounded operators in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alfredo Peris, Antonio Bonilla, Teresa Berm\\'udez, Vladimir M\\\"uller","submitted_at":"2017-06-12T13:50:00Z","abstract_excerpt":"We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing absolutely Ces\\`aro bounded operators on $\\ell^p(\\mathbb{N})$, $1\\le p < \\infty$, which are not power bounded, and provide examples of uniformly Kreiss bounded operators which are not absolutely Ces\\`aro bounded. These results complement very limited number of known examples (see \\cite{Shi} and \\cite{AS}). "},"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":"1706.03638","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-12T13:50:00Z","cross_cats_sorted":[],"title_canon_sha256":"d4bb8dc0de6bd550401bbec7c081192d05a0e7d38ff3f743586ab42809318e6d","abstract_canon_sha256":"8b50819ce69299cd201d5b8da2f45a123c67c2098b6b21f992aa6f701d3ecdc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:34.072868Z","signature_b64":"wgtmTNXEOE5gRiCaeZZVpEEKoT3V8u3P0LMdkz8YZ52XePQ3ZfcglcyFKYd4ovZKvrEb+cmvoWwQGElNMUVTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de48e30d1e9919f82ba47b0a0aa1508f89cc8c94cf24c160ebf47bdbc96d892e","last_reissued_at":"2026-05-18T00:42:34.072089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:34.072089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ces\\`aro bounded operators in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alfredo Peris, Antonio Bonilla, Teresa Berm\\'udez, Vladimir M\\\"uller","submitted_at":"2017-06-12T13:50:00Z","abstract_excerpt":"We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing absolutely Ces\\`aro bounded operators on $\\ell^p(\\mathbb{N})$, $1\\le p < \\infty$, which are not power bounded, and provide examples of uniformly Kreiss bounded operators which are not absolutely Ces\\`aro bounded. These results complement very limited number of known examples (see \\cite{Shi} and \\cite{AS}). "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03638","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":"1706.03638","created_at":"2026-05-18T00:42:34.072221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03638v1","created_at":"2026-05-18T00:42:34.072221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03638","created_at":"2026-05-18T00:42:34.072221+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ZEOGDI6TEM7","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ZEOGDI6TEM7QK5E","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ZEOGDI6","created_at":"2026-05-18T12:30:58.224056+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/3ZEOGDI6TEM7QK5EPMFAVIKQR6","json":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6.json","graph_json":"https://pith.science/api/pith-number/3ZEOGDI6TEM7QK5EPMFAVIKQR6/graph.json","events_json":"https://pith.science/api/pith-number/3ZEOGDI6TEM7QK5EPMFAVIKQR6/events.json","paper":"https://pith.science/paper/3ZEOGDI6"},"agent_actions":{"view_html":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6","download_json":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6.json","view_paper":"https://pith.science/paper/3ZEOGDI6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03638&json=true","fetch_graph":"https://pith.science/api/pith-number/3ZEOGDI6TEM7QK5EPMFAVIKQR6/graph.json","fetch_events":"https://pith.science/api/pith-number/3ZEOGDI6TEM7QK5EPMFAVIKQR6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/action/storage_attestation","attest_author":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/action/author_attestation","sign_citation":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/action/citation_signature","submit_replication":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/action/replication_record"}},"created_at":"2026-05-18T00:42:34.072221+00:00","updated_at":"2026-05-18T00:42:34.072221+00:00"}