{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:I6LA5VFDSPG3MKXU2EBV4KXSGW","short_pith_number":"pith:I6LA5VFD","schema_version":"1.0","canonical_sha256":"47960ed4a393cdb62af4d1035e2af235bfcc027eef442b1b10ae9fd410dee57d","source":{"kind":"arxiv","id":"2403.04137","version":1},"attestation_state":"computed","paper":{"title":"The compact operators on $c_0$ as a Calkin algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Daniele Puglisi, Pavlos Motakis","submitted_at":"2024-03-07T01:33:38Z","abstract_excerpt":"For a Banach space $X$, let $\\mathcal{L}(X)$ denote the algebra of all bounded linear operators on $X$ and let $\\mathcal{K}(X)$ denote the compact operator ideal in $\\mathcal{L}(X)$. The quotient algebra $\\mathcal{L}(X)/\\mathcal{K}(X)$ is called the Calkin algebra of $X$, and it is denoted $\\mathcal{C}al(X)$. We prove that the unitization of $\\mathcal{K}(c_0)$ is isomorphic as a Banach algebra to the Calkin algebra of some Banach space $\\mathcal{Z}_{\\mathcal{K}(c_0)}$. This Banach space is an Argyros-Haydon sum $(\\oplus_{n=1}^\\infty X_n)_\\mathrm{AH}$ of a sequence of copies $X_n$ of a single A"},"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":"2403.04137","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-03-07T01:33:38Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"d90d508f220c6ae481c885277735de1da1e250e720696a994d97de0e418aec4e","abstract_canon_sha256":"532ce26cad5699198aaf5cde9e0d72478422c937eaad2c25245af9cd5a8ee872"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:53:19.095169Z","signature_b64":"ldo+nLAx32tWWNg7nSvD8AKm/zfDZASi/dpuNC2e+Mr19sgM+oRDJKBYt5blnwTXU2M4W3hMqrz73j8wPUgxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47960ed4a393cdb62af4d1035e2af235bfcc027eef442b1b10ae9fd410dee57d","last_reissued_at":"2026-07-05T07:53:19.094740Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:53:19.094740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The compact operators on $c_0$ as a Calkin algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Daniele Puglisi, Pavlos Motakis","submitted_at":"2024-03-07T01:33:38Z","abstract_excerpt":"For a Banach space $X$, let $\\mathcal{L}(X)$ denote the algebra of all bounded linear operators on $X$ and let $\\mathcal{K}(X)$ denote the compact operator ideal in $\\mathcal{L}(X)$. The quotient algebra $\\mathcal{L}(X)/\\mathcal{K}(X)$ is called the Calkin algebra of $X$, and it is denoted $\\mathcal{C}al(X)$. We prove that the unitization of $\\mathcal{K}(c_0)$ is isomorphic as a Banach algebra to the Calkin algebra of some Banach space $\\mathcal{Z}_{\\mathcal{K}(c_0)}$. This Banach space is an Argyros-Haydon sum $(\\oplus_{n=1}^\\infty X_n)_\\mathrm{AH}$ of a sequence of copies $X_n$ of a single A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04137","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/2403.04137/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":"2403.04137","created_at":"2026-07-05T07:53:19.094802+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.04137v1","created_at":"2026-07-05T07:53:19.094802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.04137","created_at":"2026-07-05T07:53:19.094802+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6LA5VFDSPG3","created_at":"2026-07-05T07:53:19.094802+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6LA5VFDSPG3MKXU","created_at":"2026-07-05T07:53:19.094802+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6LA5VFD","created_at":"2026-07-05T07:53:19.094802+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/I6LA5VFDSPG3MKXU2EBV4KXSGW","json":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW.json","graph_json":"https://pith.science/api/pith-number/I6LA5VFDSPG3MKXU2EBV4KXSGW/graph.json","events_json":"https://pith.science/api/pith-number/I6LA5VFDSPG3MKXU2EBV4KXSGW/events.json","paper":"https://pith.science/paper/I6LA5VFD"},"agent_actions":{"view_html":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW","download_json":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW.json","view_paper":"https://pith.science/paper/I6LA5VFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.04137&json=true","fetch_graph":"https://pith.science/api/pith-number/I6LA5VFDSPG3MKXU2EBV4KXSGW/graph.json","fetch_events":"https://pith.science/api/pith-number/I6LA5VFDSPG3MKXU2EBV4KXSGW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW/action/storage_attestation","attest_author":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW/action/author_attestation","sign_citation":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW/action/citation_signature","submit_replication":"https://pith.science/pith/I6LA5VFDSPG3MKXU2EBV4KXSGW/action/replication_record"}},"created_at":"2026-07-05T07:53:19.094802+00:00","updated_at":"2026-07-05T07:53:19.094802+00:00"}