{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:242SFBMMEBJARBVM5OGNCNM6J4","short_pith_number":"pith:242SFBMM","schema_version":"1.0","canonical_sha256":"d73522858c20520886aceb8cd1359e4f08ceb75cd9718d5fbad48ba0f1bad88c","source":{"kind":"arxiv","id":"1404.3121","version":1},"attestation_state":"computed","paper":{"title":"The Drazin spectrum of tensor product of Banach algebra elements and elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrico Boasso","submitted_at":"2014-04-11T14:36:37Z","abstract_excerpt":"Given unital Banach algebras $A$ and $B$ and elements $a\\in A$ and $b\\in B$, the Drazin spectrun of $a\\otimes b\\in A\\overline{\\otimes} B$ will be fully characterized, where $A\\overline{\\otimes} B$ is a Banach algebra that is the completion of $A\\otimes B$ with respect to a uniform crossnorm. To this end, however, first the isolated points of the spectrum of $a\\otimes b\\in A\\overline{\\otimes} B$ need to be characterized. On the other hand, given Banach spaces $X$ and $Y$ and Banach space operators $S\\in L(X)$ and $T\\in L(Y)$, using similar arguments the Drazin spectrum of $\\tau_{ST}\\in L(L(Y,X)"},"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":"1404.3121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-11T14:36:37Z","cross_cats_sorted":[],"title_canon_sha256":"c8b4829fba0613a9f1d8bf4a7ec7ae272c48fe590855a47e52ece66a2de0beda","abstract_canon_sha256":"922d50c0cafdd947311d55890f546df171d980df0b596d0da2be1d778ece821a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:22.167010Z","signature_b64":"Gc46sa65xaTuGp1Khbfp7Jn9fAV7clxAixP8Q00pFh8E2vQSWduO4DqhlCrKx9J/YHajlrsXDkvIOpqku11aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d73522858c20520886aceb8cd1359e4f08ceb75cd9718d5fbad48ba0f1bad88c","last_reissued_at":"2026-05-18T02:54:22.166604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:22.166604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Drazin spectrum of tensor product of Banach algebra elements and elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrico Boasso","submitted_at":"2014-04-11T14:36:37Z","abstract_excerpt":"Given unital Banach algebras $A$ and $B$ and elements $a\\in A$ and $b\\in B$, the Drazin spectrun of $a\\otimes b\\in A\\overline{\\otimes} B$ will be fully characterized, where $A\\overline{\\otimes} B$ is a Banach algebra that is the completion of $A\\otimes B$ with respect to a uniform crossnorm. To this end, however, first the isolated points of the spectrum of $a\\otimes b\\in A\\overline{\\otimes} B$ need to be characterized. On the other hand, given Banach spaces $X$ and $Y$ and Banach space operators $S\\in L(X)$ and $T\\in L(Y)$, using similar arguments the Drazin spectrum of $\\tau_{ST}\\in L(L(Y,X)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3121","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":"1404.3121","created_at":"2026-05-18T02:54:22.166666+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.3121v1","created_at":"2026-05-18T02:54:22.166666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3121","created_at":"2026-05-18T02:54:22.166666+00:00"},{"alias_kind":"pith_short_12","alias_value":"242SFBMMEBJA","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"242SFBMMEBJARBVM","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"242SFBMM","created_at":"2026-05-18T12:28:09.283467+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/242SFBMMEBJARBVM5OGNCNM6J4","json":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4.json","graph_json":"https://pith.science/api/pith-number/242SFBMMEBJARBVM5OGNCNM6J4/graph.json","events_json":"https://pith.science/api/pith-number/242SFBMMEBJARBVM5OGNCNM6J4/events.json","paper":"https://pith.science/paper/242SFBMM"},"agent_actions":{"view_html":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4","download_json":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4.json","view_paper":"https://pith.science/paper/242SFBMM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.3121&json=true","fetch_graph":"https://pith.science/api/pith-number/242SFBMMEBJARBVM5OGNCNM6J4/graph.json","fetch_events":"https://pith.science/api/pith-number/242SFBMMEBJARBVM5OGNCNM6J4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4/action/storage_attestation","attest_author":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4/action/author_attestation","sign_citation":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4/action/citation_signature","submit_replication":"https://pith.science/pith/242SFBMMEBJARBVM5OGNCNM6J4/action/replication_record"}},"created_at":"2026-05-18T02:54:22.166666+00:00","updated_at":"2026-05-18T02:54:22.166666+00:00"}