{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VEDMOFFG72DR5TLDPR2ZIMTI4K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"412cf4229898fb079854c145baa3324eaab2f5573f30cf577954752ec5c7b150","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-22T06:01:38Z","title_canon_sha256":"6d4032f43b07a04397e4669a361ee73112a2593b87f8d8ed6aeea2332269a9ff"},"schema_version":"1.0","source":{"id":"1905.08962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08962","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08962v1","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08962","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"VEDMOFFG72DR","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VEDMOFFG72DR5TLD","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VEDMOFFG","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c5db1e4c2a988fc176ae53001ca4a8b92749371566230157126a110fc0f5517b","target":"graph","created_at":"2026-05-17T23:45:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that the operator obtained by the composition of the synthesis and analysis operators of two controlled g-Bessel sequence is a trace class operator. Also, we define the canonical controlled g-dual and show that this dual gives rise to expand coefficients with the minimal norm. Finally, we extend some known equality and inequalities for controlled g-frames.","authors_text":"Asghar Rahimi, Elnaz Osgooei, Maryam Forughi, Mojgan Javahernia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-22T06:01:38Z","title":"An appropriate representation space for controlled G-frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08962","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:85369355766f310c74901d1b56d1d52d10a7970612afa8d3cba1dedd3881c97f","target":"record","created_at":"2026-05-17T23:45:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"412cf4229898fb079854c145baa3324eaab2f5573f30cf577954752ec5c7b150","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-22T06:01:38Z","title_canon_sha256":"6d4032f43b07a04397e4669a361ee73112a2593b87f8d8ed6aeea2332269a9ff"},"schema_version":"1.0","source":{"id":"1905.08962","kind":"arxiv","version":1}},"canonical_sha256":"a906c714a6fe871ecd637c75943268e2906cf16cf8c72cc4189a113e915c04dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a906c714a6fe871ecd637c75943268e2906cf16cf8c72cc4189a113e915c04dd","first_computed_at":"2026-05-17T23:45:24.748175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:24.748175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BiW2xRTKuSJYvGEf6+gfWn5k1sl218Fs/NM2T+lTpA9sAoF8RYi0DQG/E+Is93bUym1S0esbeyLgVDmY8l3sAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:24.748589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.08962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85369355766f310c74901d1b56d1d52d10a7970612afa8d3cba1dedd3881c97f","sha256:c5db1e4c2a988fc176ae53001ca4a8b92749371566230157126a110fc0f5517b"],"state_sha256":"17fcfe6395fa2f31b15b4d2bf07344814e86aed060015aefe6e880842d0e683b"}