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This implies that if for every Hilbert $C^*$-module $E$ over a $C^*$-algebra $\\mathcal{A}$, the algebra $B(E)$ of adjointable operators on $E$ is a $ W^*$-algebra, then $\\mathcal{A}$ is a $C^*$-algebra of compact operators.\n  Also we show that a unital $C^*$-algebra $\\mathcal{A}$ which is Morita equivalent to a $ W^*$-algebra must be a $ W^*$-algebra."},"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":"1304.7453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-28T10:54:52Z","cross_cats_sorted":[],"title_canon_sha256":"348e249a97119ee3e8b601a506a7d4849622cbcb8f7d7f70c6f3995af5813944","abstract_canon_sha256":"eb4aa5384436c757983f29dbd71ceddfa8c2249cd6e934a14dbb83779f80ac46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:53.935105Z","signature_b64":"UTmYcK/4DG01v+Bd55OrGY6fY1imLGcHgFlM0iw0miaT02INfxyB2BGq4WS/ovRwSMu2K1qGH7wgxFbgbhOSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"474710889f626366071815fcd6223b85ba6c3de75a43fe1385634add1d5f8e6d","last_reissued_at":"2026-05-18T03:26:53.934449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:53.934449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Which multiplier algebras are $W^*$-algebras?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Charles A. Akemann, Massoud Amini, Mohammad B. Asadi","submitted_at":"2013-04-28T10:54:52Z","abstract_excerpt":"We consider the question of when the multiplier algebra $M(\\mathcal{A})$ of a $C^*$-algebra $\\mathcal{A}$ is a $ W^*$-algebra, and show that it holds for a stable $C^*$-algebra exactly when it is a $C^*$-algebra of compact operators. This implies that if for every Hilbert $C^*$-module $E$ over a $C^*$-algebra $\\mathcal{A}$, the algebra $B(E)$ of adjointable operators on $E$ is a $ W^*$-algebra, then $\\mathcal{A}$ is a $C^*$-algebra of compact operators.\n  Also we show that a unital $C^*$-algebra $\\mathcal{A}$ which is Morita equivalent to a $ W^*$-algebra must be a $ W^*$-algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7453","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":"1304.7453","created_at":"2026-05-18T03:26:53.934570+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7453v1","created_at":"2026-05-18T03:26:53.934570+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7453","created_at":"2026-05-18T03:26:53.934570+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5DRBCE7MJRW","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5DRBCE7MJRWMBYY","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5DRBCE7","created_at":"2026-05-18T12:27:46.883200+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/I5DRBCE7MJRWMBYYCX6NMIR3QW","json":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW.json","graph_json":"https://pith.science/api/pith-number/I5DRBCE7MJRWMBYYCX6NMIR3QW/graph.json","events_json":"https://pith.science/api/pith-number/I5DRBCE7MJRWMBYYCX6NMIR3QW/events.json","paper":"https://pith.science/paper/I5DRBCE7"},"agent_actions":{"view_html":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW","download_json":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW.json","view_paper":"https://pith.science/paper/I5DRBCE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7453&json=true","fetch_graph":"https://pith.science/api/pith-number/I5DRBCE7MJRWMBYYCX6NMIR3QW/graph.json","fetch_events":"https://pith.science/api/pith-number/I5DRBCE7MJRWMBYYCX6NMIR3QW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW/action/storage_attestation","attest_author":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW/action/author_attestation","sign_citation":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW/action/citation_signature","submit_replication":"https://pith.science/pith/I5DRBCE7MJRWMBYYCX6NMIR3QW/action/replication_record"}},"created_at":"2026-05-18T03:26:53.934570+00:00","updated_at":"2026-05-18T03:26:53.934570+00:00"}