{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4T37IZXX7CAKWV4C55RXGZP4XF","short_pith_number":"pith:4T37IZXX","schema_version":"1.0","canonical_sha256":"e4f7f466f7f880ab5782ef637365fcb97af57fe591a273492d39d818902d8dc5","source":{"kind":"arxiv","id":"1602.04173","version":1},"attestation_state":"computed","paper":{"title":"Limited operators and differentiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammed Bachir","submitted_at":"2016-02-12T19:17:02Z","abstract_excerpt":"We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous operator $T: Y \\longrightarrow X$, we prove that   $T$ is a limited operator if and only if, for every convex continuous function $f: X \\longrightarrow \\R$ and every point $y\\in Y$, $f\\circ T$ is Fr\\'echet differentiable at $y\\in Y$ whenever $f$ is G\\^ateaux differentiable at $T(y)\\in X$."},"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":"1602.04173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-02-12T19:17:02Z","cross_cats_sorted":[],"title_canon_sha256":"6b0bfdf09be9545a6039461ba4fbe3ff2e2509176462cf3d43652c7b44f73dee","abstract_canon_sha256":"ef0f4afd9e398c2af1930985dc635ba0c8e0d09f923c4246e7b7157c24b24d96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.363169Z","signature_b64":"cYy0nahud0Nn8AHTqRkCww12kJwzRR+OKGEzapSMadNqrcWkbhlmdGxyVWtRZumBUWqFlrFfYAtGJNKRGWe1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4f7f466f7f880ab5782ef637365fcb97af57fe591a273492d39d818902d8dc5","last_reissued_at":"2026-05-18T01:20:54.362484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.362484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limited operators and differentiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammed Bachir","submitted_at":"2016-02-12T19:17:02Z","abstract_excerpt":"We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous operator $T: Y \\longrightarrow X$, we prove that   $T$ is a limited operator if and only if, for every convex continuous function $f: X \\longrightarrow \\R$ and every point $y\\in Y$, $f\\circ T$ is Fr\\'echet differentiable at $y\\in Y$ whenever $f$ is G\\^ateaux differentiable at $T(y)\\in X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04173","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":"1602.04173","created_at":"2026-05-18T01:20:54.362578+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.04173v1","created_at":"2026-05-18T01:20:54.362578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04173","created_at":"2026-05-18T01:20:54.362578+00:00"},{"alias_kind":"pith_short_12","alias_value":"4T37IZXX7CAK","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4T37IZXX7CAKWV4C","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4T37IZXX","created_at":"2026-05-18T12:29:58.707656+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/4T37IZXX7CAKWV4C55RXGZP4XF","json":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF.json","graph_json":"https://pith.science/api/pith-number/4T37IZXX7CAKWV4C55RXGZP4XF/graph.json","events_json":"https://pith.science/api/pith-number/4T37IZXX7CAKWV4C55RXGZP4XF/events.json","paper":"https://pith.science/paper/4T37IZXX"},"agent_actions":{"view_html":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF","download_json":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF.json","view_paper":"https://pith.science/paper/4T37IZXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.04173&json=true","fetch_graph":"https://pith.science/api/pith-number/4T37IZXX7CAKWV4C55RXGZP4XF/graph.json","fetch_events":"https://pith.science/api/pith-number/4T37IZXX7CAKWV4C55RXGZP4XF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF/action/storage_attestation","attest_author":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF/action/author_attestation","sign_citation":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF/action/citation_signature","submit_replication":"https://pith.science/pith/4T37IZXX7CAKWV4C55RXGZP4XF/action/replication_record"}},"created_at":"2026-05-18T01:20:54.362578+00:00","updated_at":"2026-05-18T01:20:54.362578+00:00"}