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We construct two unital algebra and order continuous Riesz homomorphisms \\[ \\gamma:((Orth(E))^{\\sim})_{n}^{\\sim}\\rightarrow Orth(E^{\\sim})\\text{ }% \\] and \\[ m:Z(E)^{\\prime\\prime}\\rightarrow Z(E^{\\sim}) \\] that extend the above mentioned natural inclusions respectively. Then, the range of $\\gamma$ is an order ideal in $Orth(E^{\\sim})$ if and only if $m$ is surjective. Furthermore, $"},"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":"1406.6335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-24T19:00:51Z","cross_cats_sorted":[],"title_canon_sha256":"25ea01832775e1c46c10fc0877ee0222bdc26b79263b2d9b1c4d01cc9ed6dd9d","abstract_canon_sha256":"e4fd45915437c38f968e11a42dcaed6e955efaad6fcf7441ba5f213e212011ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:03.650883Z","signature_b64":"y5rsvJxkFTu1VR27mQmIuryDfbmE91Dwl4s7kzDfXx6BfUJ3/K1KBM73ClP4cQLVGpd0q+xkfiH6jgrnZNBQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9d189e0df37ca32776db7460de0c02109c32dae27faae2a7c30cfff387dcc1f","last_reissued_at":"2026-05-18T02:49:03.650413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:03.650413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of Riesz spaces with topologically full center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"\\c{S}afak Alpay, Mehmet Orhon","submitted_at":"2014-06-24T19:00:51Z","abstract_excerpt":"Let $E$ be a Riesz space and let $E^{\\sim}$ denote its order dual. The orthomorphisms $Orth(E)$ on $E,$ and the ideal center $Z(E)$ of $E,$ are naturally embedded in $Orth(E^{\\sim})$ and $Z(E^{\\sim})$ respectively. We construct two unital algebra and order continuous Riesz homomorphisms \\[ \\gamma:((Orth(E))^{\\sim})_{n}^{\\sim}\\rightarrow Orth(E^{\\sim})\\text{ }% \\] and \\[ m:Z(E)^{\\prime\\prime}\\rightarrow Z(E^{\\sim}) \\] that extend the above mentioned natural inclusions respectively. Then, the range of $\\gamma$ is an order ideal in $Orth(E^{\\sim})$ if and only if $m$ is surjective. Furthermore, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6335","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":"1406.6335","created_at":"2026-05-18T02:49:03.650473+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.6335v1","created_at":"2026-05-18T02:49:03.650473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6335","created_at":"2026-05-18T02:49:03.650473+00:00"},{"alias_kind":"pith_short_12","alias_value":"3HIYTYG7G7FD","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3HIYTYG7G7FDE53N","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3HIYTYG7","created_at":"2026-05-18T12:28:11.866339+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/3HIYTYG7G7FDE53NW5DA3YGAEE","json":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE.json","graph_json":"https://pith.science/api/pith-number/3HIYTYG7G7FDE53NW5DA3YGAEE/graph.json","events_json":"https://pith.science/api/pith-number/3HIYTYG7G7FDE53NW5DA3YGAEE/events.json","paper":"https://pith.science/paper/3HIYTYG7"},"agent_actions":{"view_html":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE","download_json":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE.json","view_paper":"https://pith.science/paper/3HIYTYG7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.6335&json=true","fetch_graph":"https://pith.science/api/pith-number/3HIYTYG7G7FDE53NW5DA3YGAEE/graph.json","fetch_events":"https://pith.science/api/pith-number/3HIYTYG7G7FDE53NW5DA3YGAEE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE/action/storage_attestation","attest_author":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE/action/author_attestation","sign_citation":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE/action/citation_signature","submit_replication":"https://pith.science/pith/3HIYTYG7G7FDE53NW5DA3YGAEE/action/replication_record"}},"created_at":"2026-05-18T02:49:03.650473+00:00","updated_at":"2026-05-18T02:49:03.650473+00:00"}