{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3ZEOGDI6TEM7QK5EPMFAVIKQR6","short_pith_number":"pith:3ZEOGDI6","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"},"canonical_sha256":"de48e30d1e9919f82ba47b0a0aa1508f89cc8c94cf24c160ebf47bdbc96d892e","source":{"kind":"arxiv","id":"1706.03638","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03638","created_at":"2026-05-18T00:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03638v1","created_at":"2026-05-18T00:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03638","created_at":"2026-05-18T00:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"3ZEOGDI6TEM7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ZEOGDI6TEM7QK5E","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ZEOGDI6","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3ZEOGDI6TEM7QK5EPMFAVIKQR6","target":"record","payload":{"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"},"canonical_sha256":"de48e30d1e9919f82ba47b0a0aa1508f89cc8c94cf24c160ebf47bdbc96d892e","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"},"source_kind":"arxiv","source_id":"1706.03638","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"srzVmWzyDeaGY9J/DLGznQQSKYCgl4wr6SYEWWKYxDrp9318NJLemCk2rlzDZdtPqCZtcTz6s8PFIlHUdO7qCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:17:54.718799Z"},"content_sha256":"94a47181c634ffaf39022fbcc6c682ae1fe539d03c8c5f993c76a15d4d84cb80","schema_version":"1.0","event_id":"sha256:94a47181c634ffaf39022fbcc6c682ae1fe539d03c8c5f993c76a15d4d84cb80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3ZEOGDI6TEM7QK5EPMFAVIKQR6","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UlQ6Q2OgNAiHL3EksPELrukpPjIYx3Dn8hivutUtaB95GImbpKA8Pr7YriKBOtNxag4nOYOIm3Ae2PLq54EcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:17:54.719427Z"},"content_sha256":"11d21be0ebc26990e503a138618c05da907e380d1719e5e369c69566fea45fd2","schema_version":"1.0","event_id":"sha256:11d21be0ebc26990e503a138618c05da907e380d1719e5e369c69566fea45fd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/bundle.json","state_url":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T13:17:54Z","links":{"resolver":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6","bundle":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/bundle.json","state":"https://pith.science/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ZEOGDI6TEM7QK5EPMFAVIKQR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3ZEOGDI6TEM7QK5EPMFAVIKQR6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8b50819ce69299cd201d5b8da2f45a123c67c2098b6b21f992aa6f701d3ecdc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-12T13:50:00Z","title_canon_sha256":"d4bb8dc0de6bd550401bbec7c081192d05a0e7d38ff3f743586ab42809318e6d"},"schema_version":"1.0","source":{"id":"1706.03638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03638","created_at":"2026-05-18T00:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03638v1","created_at":"2026-05-18T00:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03638","created_at":"2026-05-18T00:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"3ZEOGDI6TEM7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ZEOGDI6TEM7QK5E","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ZEOGDI6","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:11d21be0ebc26990e503a138618c05da907e380d1719e5e369c69566fea45fd2","target":"graph","created_at":"2026-05-18T00:42:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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}). ","authors_text":"Alfredo Peris, Antonio Bonilla, Teresa Berm\\'udez, Vladimir M\\\"uller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-12T13:50:00Z","title":"Ces\\`aro bounded operators in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03638","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:94a47181c634ffaf39022fbcc6c682ae1fe539d03c8c5f993c76a15d4d84cb80","target":"record","created_at":"2026-05-18T00:42:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8b50819ce69299cd201d5b8da2f45a123c67c2098b6b21f992aa6f701d3ecdc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-12T13:50:00Z","title_canon_sha256":"d4bb8dc0de6bd550401bbec7c081192d05a0e7d38ff3f743586ab42809318e6d"},"schema_version":"1.0","source":{"id":"1706.03638","kind":"arxiv","version":1}},"canonical_sha256":"de48e30d1e9919f82ba47b0a0aa1508f89cc8c94cf24c160ebf47bdbc96d892e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de48e30d1e9919f82ba47b0a0aa1508f89cc8c94cf24c160ebf47bdbc96d892e","first_computed_at":"2026-05-18T00:42:34.072089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:34.072089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgtmTNXEOE5gRiCaeZZVpEEKoT3V8u3P0LMdkz8YZ52XePQ3ZfcglcyFKYd4ovZKvrEb+cmvoWwQGElNMUVTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:34.072868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94a47181c634ffaf39022fbcc6c682ae1fe539d03c8c5f993c76a15d4d84cb80","sha256:11d21be0ebc26990e503a138618c05da907e380d1719e5e369c69566fea45fd2"],"state_sha256":"0a4c617426ae87564d6095b4c21a0d73d64d8d141bcd03369ef038a8f29174c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ig27NozDf5qMu/9LuBRyyIijgPCQ0aP6mil4+zdASdt+CqvlqK6totkFmId40iBVg4V2FZDwiwKd43MB8bgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:17:54.723010Z","bundle_sha256":"aaaa106403c239c51444ff7251ffd2b47759f911420a5e8a1fc15c9a8d5a3d3a"}}