{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:B72R7PCEWOWSVFD3JYDMZZTW3O","short_pith_number":"pith:B72R7PCE","schema_version":"1.0","canonical_sha256":"0ff51fbc44b3ad2a947b4e06cce676dbb871e51839c298842bafa84fa58b4585","source":{"kind":"arxiv","id":"1704.04665","version":1},"attestation_state":"computed","paper":{"title":"The unit ball of an injective operator space has an extreme point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Masayoshi Kaneda","submitted_at":"2017-04-15T17:24:37Z","abstract_excerpt":"We define an $AW^*$-TRO as an off-diagonal corner of an $AW^*$-algebra, and show that the unit ball of an $AW^*$-TRO has an extreme point. In particular, the unit ball of an injective operator space has an extreme point, which answers a question raised in the author's previous work [Journal of Operator Theory, 76(2) (2016), 219-248] affirmatively. We also show that an $AW^*$-TRO (respectively, an injective operator space) has an ideal decomposition, that is, it can be decomposed into the direct sum of a left ideal, a right ideal, and a two-sided ideal in an $AW^*$-algebra (respectively, an inj"},"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":"1704.04665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-15T17:24:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"db3fb5d45352dc54f24cef6aaa764b17790591d0c42fb22276ab61bd2a291751","abstract_canon_sha256":"fc315f2ce16005467fa3d4a1b44bca0e4b5b005a5daddcfde05ebfef6493351e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:17.978722Z","signature_b64":"LtqQcA8vQLHIa2WC+ADsS7Ghwmw5024GezB51uREHjX1IZSZjAP19IQqKkiObXgidj6L0JxDu9VZOEfX7WITBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff51fbc44b3ad2a947b4e06cce676dbb871e51839c298842bafa84fa58b4585","last_reissued_at":"2026-05-18T00:46:17.978363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:17.978363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The unit ball of an injective operator space has an extreme point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Masayoshi Kaneda","submitted_at":"2017-04-15T17:24:37Z","abstract_excerpt":"We define an $AW^*$-TRO as an off-diagonal corner of an $AW^*$-algebra, and show that the unit ball of an $AW^*$-TRO has an extreme point. In particular, the unit ball of an injective operator space has an extreme point, which answers a question raised in the author's previous work [Journal of Operator Theory, 76(2) (2016), 219-248] affirmatively. We also show that an $AW^*$-TRO (respectively, an injective operator space) has an ideal decomposition, that is, it can be decomposed into the direct sum of a left ideal, a right ideal, and a two-sided ideal in an $AW^*$-algebra (respectively, an inj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04665","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":"1704.04665","created_at":"2026-05-18T00:46:17.978427+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.04665v1","created_at":"2026-05-18T00:46:17.978427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04665","created_at":"2026-05-18T00:46:17.978427+00:00"},{"alias_kind":"pith_short_12","alias_value":"B72R7PCEWOWS","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"B72R7PCEWOWSVFD3","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"B72R7PCE","created_at":"2026-05-18T12:31:08.081275+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/B72R7PCEWOWSVFD3JYDMZZTW3O","json":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O.json","graph_json":"https://pith.science/api/pith-number/B72R7PCEWOWSVFD3JYDMZZTW3O/graph.json","events_json":"https://pith.science/api/pith-number/B72R7PCEWOWSVFD3JYDMZZTW3O/events.json","paper":"https://pith.science/paper/B72R7PCE"},"agent_actions":{"view_html":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O","download_json":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O.json","view_paper":"https://pith.science/paper/B72R7PCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.04665&json=true","fetch_graph":"https://pith.science/api/pith-number/B72R7PCEWOWSVFD3JYDMZZTW3O/graph.json","fetch_events":"https://pith.science/api/pith-number/B72R7PCEWOWSVFD3JYDMZZTW3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O/action/storage_attestation","attest_author":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O/action/author_attestation","sign_citation":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O/action/citation_signature","submit_replication":"https://pith.science/pith/B72R7PCEWOWSVFD3JYDMZZTW3O/action/replication_record"}},"created_at":"2026-05-18T00:46:17.978427+00:00","updated_at":"2026-05-18T00:46:17.978427+00:00"}