{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:REZ6R7GVU6YZBEODOFEOTR757L","short_pith_number":"pith:REZ6R7GV","schema_version":"1.0","canonical_sha256":"8933e8fcd5a7b19091c37148e9c7fdfade6b413c7f658da0b5a16a44a20a80f1","source":{"kind":"arxiv","id":"1410.2700","version":2},"attestation_state":"computed","paper":{"title":"A review of some works in the theory of diskcyclic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adem K{\\i}l{\\i}\\c{c}man, Mohd Salmi Md Noorani, Nareen Bamerni","submitted_at":"2014-10-10T07:47:50Z","abstract_excerpt":"In this paper, we give a brief review concerning diskcyclic operators and then we provide some further characterizations of diskcyclic operators on separable Hilbert spaces. In particular, we show that if $x\\in {\\mathcal H}$ has a disk orbit under $T$ that is somewhere dense in ${\\mathcal H}$ then the disk orbit of $x$ under $T$ need not be everywhere dense in ${\\mathcal H}$. We also show that the inverse and the adjoint of a diskcyclic operator need not be diskcyclic. Moreover, we establish another diskcyclicity criterion and use it to find a necessary and sufficient condition for unilateral "},"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":"1410.2700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-10T07:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"2f6f1f4009b9c0a8a33dfc0c1a3a46d8a183ecb90d7a9f2dd201d8acc5fb764e","abstract_canon_sha256":"efcb59ad45a8fc1b0919f3a63ef3fa7ab9855586c921d456ff6db3cf3f389809"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:23.227797Z","signature_b64":"TOs/J8W+bnQaq2evLRiIlPUGn4THtljc/tDrO5HrQrACzeNi5Me/0XhAUUmV51TalypaD9f2NZYDiIXNswx2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8933e8fcd5a7b19091c37148e9c7fdfade6b413c7f658da0b5a16a44a20a80f1","last_reissued_at":"2026-05-18T02:29:23.227328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:23.227328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A review of some works in the theory of diskcyclic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adem K{\\i}l{\\i}\\c{c}man, Mohd Salmi Md Noorani, Nareen Bamerni","submitted_at":"2014-10-10T07:47:50Z","abstract_excerpt":"In this paper, we give a brief review concerning diskcyclic operators and then we provide some further characterizations of diskcyclic operators on separable Hilbert spaces. In particular, we show that if $x\\in {\\mathcal H}$ has a disk orbit under $T$ that is somewhere dense in ${\\mathcal H}$ then the disk orbit of $x$ under $T$ need not be everywhere dense in ${\\mathcal H}$. We also show that the inverse and the adjoint of a diskcyclic operator need not be diskcyclic. Moreover, we establish another diskcyclicity criterion and use it to find a necessary and sufficient condition for unilateral "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2700","kind":"arxiv","version":2},"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":"1410.2700","created_at":"2026-05-18T02:29:23.227400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2700v2","created_at":"2026-05-18T02:29:23.227400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2700","created_at":"2026-05-18T02:29:23.227400+00:00"},{"alias_kind":"pith_short_12","alias_value":"REZ6R7GVU6YZ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"REZ6R7GVU6YZBEOD","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"REZ6R7GV","created_at":"2026-05-18T12:28:46.137349+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/REZ6R7GVU6YZBEODOFEOTR757L","json":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L.json","graph_json":"https://pith.science/api/pith-number/REZ6R7GVU6YZBEODOFEOTR757L/graph.json","events_json":"https://pith.science/api/pith-number/REZ6R7GVU6YZBEODOFEOTR757L/events.json","paper":"https://pith.science/paper/REZ6R7GV"},"agent_actions":{"view_html":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L","download_json":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L.json","view_paper":"https://pith.science/paper/REZ6R7GV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2700&json=true","fetch_graph":"https://pith.science/api/pith-number/REZ6R7GVU6YZBEODOFEOTR757L/graph.json","fetch_events":"https://pith.science/api/pith-number/REZ6R7GVU6YZBEODOFEOTR757L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L/action/storage_attestation","attest_author":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L/action/author_attestation","sign_citation":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L/action/citation_signature","submit_replication":"https://pith.science/pith/REZ6R7GVU6YZBEODOFEOTR757L/action/replication_record"}},"created_at":"2026-05-18T02:29:23.227400+00:00","updated_at":"2026-05-18T02:29:23.227400+00:00"}