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More precisely, let $\\mathfrak{A}$ be a unital $C^*$-algebra with the unit $1$, let $a \\in \\mathfrak{A}$ be fixed such that $a, 1-a$ are invertible and let $\\mathscr{E}, \\mathscr{F}, \\mathscr{G}$ be inner product $\\mathfrak{A}$-modules. We prove that if there exist additive mappings $\\varphi, \\psi$ from $\\mathscr{F}$ into $\\mathscr{E}$ such that $\\big\\langle \\varphi(y), \\psi(z)\\big\\rangle=0$ and $a \\big\\langle \\varphi(y), \\varphi(z)\\big\\rangle a^\\ast = (1 - a)\\big\\langle \\psi(y), \\psi(z"},"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":"1811.07148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-17T12:02:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c33e8545c7cfa3b382a2154f335152cc7cd01cbe0f0e05245e3e591660858411","abstract_canon_sha256":"09abd2ff7ddabeb1da04799bed13e716de338d6e6c6e5a58ad481eabe53a60aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:28.809423Z","signature_b64":"CUu1Qszd+noavfVHgI2df99QpMcVoJgFVN/JIEBL/g6Kz3Bb3oA8E2JcK2W0nsmE1owLecquvD5tzjh3uqojDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b73f6c32f959f6c453f05340fa24df8687b89fc456a331255daa9a9d9aa5a546","last_reissued_at":"2026-05-18T00:00:28.808723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:28.808723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonally $a$-Jensen mappings on $C^*$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Ali Zamani","submitted_at":"2018-11-17T12:02:47Z","abstract_excerpt":"We investigate the representation of the so-called orthogonally $a$-Jensen mappings acting on $C^*$-modules. More precisely, let $\\mathfrak{A}$ be a unital $C^*$-algebra with the unit $1$, let $a \\in \\mathfrak{A}$ be fixed such that $a, 1-a$ are invertible and let $\\mathscr{E}, \\mathscr{F}, \\mathscr{G}$ be inner product $\\mathfrak{A}$-modules. We prove that if there exist additive mappings $\\varphi, \\psi$ from $\\mathscr{F}$ into $\\mathscr{E}$ such that $\\big\\langle \\varphi(y), \\psi(z)\\big\\rangle=0$ and $a \\big\\langle \\varphi(y), \\varphi(z)\\big\\rangle a^\\ast = (1 - a)\\big\\langle \\psi(y), \\psi(z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07148","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":"1811.07148","created_at":"2026-05-18T00:00:28.808837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.07148v1","created_at":"2026-05-18T00:00:28.808837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07148","created_at":"2026-05-18T00:00:28.808837+00:00"},{"alias_kind":"pith_short_12","alias_value":"W47WYMXZLH3M","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"W47WYMXZLH3MIU7Q","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"W47WYMXZ","created_at":"2026-05-18T12:32:59.047623+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/W47WYMXZLH3MIU7QKNAPUJG7Q2","json":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2.json","graph_json":"https://pith.science/api/pith-number/W47WYMXZLH3MIU7QKNAPUJG7Q2/graph.json","events_json":"https://pith.science/api/pith-number/W47WYMXZLH3MIU7QKNAPUJG7Q2/events.json","paper":"https://pith.science/paper/W47WYMXZ"},"agent_actions":{"view_html":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2","download_json":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2.json","view_paper":"https://pith.science/paper/W47WYMXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.07148&json=true","fetch_graph":"https://pith.science/api/pith-number/W47WYMXZLH3MIU7QKNAPUJG7Q2/graph.json","fetch_events":"https://pith.science/api/pith-number/W47WYMXZLH3MIU7QKNAPUJG7Q2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2/action/storage_attestation","attest_author":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2/action/author_attestation","sign_citation":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2/action/citation_signature","submit_replication":"https://pith.science/pith/W47WYMXZLH3MIU7QKNAPUJG7Q2/action/replication_record"}},"created_at":"2026-05-18T00:00:28.808837+00:00","updated_at":"2026-05-18T00:00:28.808837+00:00"}