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Curto, Sang Hoon Lee","submitted_at":"2019-10-19T19:20:02Z","abstract_excerpt":"Let $\\mathbf{T} \\equiv (T_1,\\cdots,T_n)$ be a commuting $n$-tuple of operators on a Hilbert space $\\mathcal{H}$, and let $T_i \\equiv V_i P \\; (1 \\le i \\le n)$ be its canonical joint polar decomposition (i.e., $P:=\\sqrt{T_1^*T_1+\\cdots+T_n^*T_n}$, $(V_1,\\cdots,V_n)$ a joint partial isometry, and $\\bigcap_{i=1}^n \\ker T_i = \\bigcap_{i=1}^n \\ker V_i = \\ker P)$. \\ The spherical Aluthge transform of $\\mathbf{T}$ is the (necessarily commuting) $n$-tuple $\\hat{\\mathbf{T}}:=(\\sqrt{P}V_1\\sqrt{P},\\cdots,\\sqrt{P}V_n\\sqrt{P})$. \\ We prove that $\\sigma_T(\\hat{\\mathbf{T}})=\\sigma_T(\\mathbf{T})$, where $\\sig"},"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":"1910.08824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-19T19:20:02Z","cross_cats_sorted":[],"title_canon_sha256":"53232793e02d846a2083870a40036cb76a66c84bff48bd3da97f5054fe563415","abstract_canon_sha256":"9129ac93dc8ebac460d2581952abe101e1ede798b360638ebd9d682bda03adb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:11.098344Z","signature_b64":"r4h0EJNvKlIEDWb0UZ2by7ItDArju0K5KhV3SAgHydQgqPO9gPcPdIiU9/wAPxu0DmvqRehVqUtrUTVymLAODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe45b65ec346770771295db4e1beae43d59e8cc555ff0210883676e8ae8f04e","last_reissued_at":"2026-06-23T02:13:11.097832Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:11.097832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Joint spectra of spherical Aluthge transforms of commuting n-tuples of Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chafiq Benhida, Jasang Yoon, Raul E. Curto, Sang Hoon Lee","submitted_at":"2019-10-19T19:20:02Z","abstract_excerpt":"Let $\\mathbf{T} \\equiv (T_1,\\cdots,T_n)$ be a commuting $n$-tuple of operators on a Hilbert space $\\mathcal{H}$, and let $T_i \\equiv V_i P \\; (1 \\le i \\le n)$ be its canonical joint polar decomposition (i.e., $P:=\\sqrt{T_1^*T_1+\\cdots+T_n^*T_n}$, $(V_1,\\cdots,V_n)$ a joint partial isometry, and $\\bigcap_{i=1}^n \\ker T_i = \\bigcap_{i=1}^n \\ker V_i = \\ker P)$. \\ The spherical Aluthge transform of $\\mathbf{T}$ is the (necessarily commuting) $n$-tuple $\\hat{\\mathbf{T}}:=(\\sqrt{P}V_1\\sqrt{P},\\cdots,\\sqrt{P}V_n\\sqrt{P})$. \\ We prove that $\\sigma_T(\\hat{\\mathbf{T}})=\\sigma_T(\\mathbf{T})$, where $\\sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.08824","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.08824/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1910.08824","created_at":"2026-06-23T02:13:11.097929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.08824v1","created_at":"2026-06-23T02:13:11.097929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.08824","created_at":"2026-06-23T02:13:11.097929+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPSFWZPMGRTX","created_at":"2026-06-23T02:13:11.097929+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPSFWZPMGRTXA5YS","created_at":"2026-06-23T02:13:11.097929+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPSFWZPM","created_at":"2026-06-23T02:13:11.097929+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/VPSFWZPMGRTXA5YSSXNU4G7K4Q","json":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q.json","graph_json":"https://pith.science/api/pith-number/VPSFWZPMGRTXA5YSSXNU4G7K4Q/graph.json","events_json":"https://pith.science/api/pith-number/VPSFWZPMGRTXA5YSSXNU4G7K4Q/events.json","paper":"https://pith.science/paper/VPSFWZPM"},"agent_actions":{"view_html":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q","download_json":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q.json","view_paper":"https://pith.science/paper/VPSFWZPM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.08824&json=true","fetch_graph":"https://pith.science/api/pith-number/VPSFWZPMGRTXA5YSSXNU4G7K4Q/graph.json","fetch_events":"https://pith.science/api/pith-number/VPSFWZPMGRTXA5YSSXNU4G7K4Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q/action/storage_attestation","attest_author":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q/action/author_attestation","sign_citation":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q/action/citation_signature","submit_replication":"https://pith.science/pith/VPSFWZPMGRTXA5YSSXNU4G7K4Q/action/replication_record"}},"created_at":"2026-06-23T02:13:11.097929+00:00","updated_at":"2026-06-23T02:13:11.097929+00:00"}