{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RYBE3KU6NLVO3HFSUOAXXSLUFU","short_pith_number":"pith:RYBE3KU6","schema_version":"1.0","canonical_sha256":"8e024daa9e6aeaed9cb2a3817bc9742d0ae58dbf23b33d99e3458df291ad3600","source":{"kind":"arxiv","id":"1810.01629","version":1},"attestation_state":"computed","paper":{"title":"Extension of frames and bases - I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"K. Mahesh Krishna, P. Sam Johnson","submitted_at":"2018-10-03T08:26:26Z","abstract_excerpt":"We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp. bases) for Banach spaces. We give a characterization for the operator-valued frames indexed by a group-like unitary system. This answers an open question asked in the paper titled \"Operator-valued frames\" by Kaftal, Larson, and Zhang in \\textit{Trans. Amer. Math. Soc.} (2009). We study stability of the extension. We also extend Riesz-Fischer theorem, Bessel'"},"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":"1810.01629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-10-03T08:26:26Z","cross_cats_sorted":[],"title_canon_sha256":"288e2f7611f32fb1bfd2574ec8767c02133dd956c21a11f30e6a4a3dc75162e7","abstract_canon_sha256":"efd1b7a77dfbea32e998ab4b1934244312b664fed8e7d4f7536658705ad26c4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:11.439365Z","signature_b64":"GblaiMBeQdWfFqRbzxVk1UFymgjF9hQiQeQRTDPRv+kB0CRMi8xuD/BX82xFOjTvJqbm6taqgfA0OqcepsodBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e024daa9e6aeaed9cb2a3817bc9742d0ae58dbf23b33d99e3458df291ad3600","last_reissued_at":"2026-05-18T00:04:11.438708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:11.438708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension of frames and bases - I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"K. Mahesh Krishna, P. Sam Johnson","submitted_at":"2018-10-03T08:26:26Z","abstract_excerpt":"We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp. bases) for Banach spaces. We give a characterization for the operator-valued frames indexed by a group-like unitary system. This answers an open question asked in the paper titled \"Operator-valued frames\" by Kaftal, Larson, and Zhang in \\textit{Trans. Amer. Math. Soc.} (2009). We study stability of the extension. We also extend Riesz-Fischer theorem, Bessel'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01629","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":"1810.01629","created_at":"2026-05-18T00:04:11.438795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01629v1","created_at":"2026-05-18T00:04:11.438795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01629","created_at":"2026-05-18T00:04:11.438795+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYBE3KU6NLVO","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYBE3KU6NLVO3HFS","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYBE3KU6","created_at":"2026-05-18T12:32:50.500415+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/RYBE3KU6NLVO3HFSUOAXXSLUFU","json":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU.json","graph_json":"https://pith.science/api/pith-number/RYBE3KU6NLVO3HFSUOAXXSLUFU/graph.json","events_json":"https://pith.science/api/pith-number/RYBE3KU6NLVO3HFSUOAXXSLUFU/events.json","paper":"https://pith.science/paper/RYBE3KU6"},"agent_actions":{"view_html":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU","download_json":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU.json","view_paper":"https://pith.science/paper/RYBE3KU6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01629&json=true","fetch_graph":"https://pith.science/api/pith-number/RYBE3KU6NLVO3HFSUOAXXSLUFU/graph.json","fetch_events":"https://pith.science/api/pith-number/RYBE3KU6NLVO3HFSUOAXXSLUFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU/action/storage_attestation","attest_author":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU/action/author_attestation","sign_citation":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU/action/citation_signature","submit_replication":"https://pith.science/pith/RYBE3KU6NLVO3HFSUOAXXSLUFU/action/replication_record"}},"created_at":"2026-05-18T00:04:11.438795+00:00","updated_at":"2026-05-18T00:04:11.438795+00:00"}