{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NDI3AKLAFL5W2O53YCEESZCSOU","short_pith_number":"pith:NDI3AKLA","schema_version":"1.0","canonical_sha256":"68d1b029602afb6d3bbbc08849645275371ce77384ae9e8862360a257ae30629","source":{"kind":"arxiv","id":"1708.05951","version":1},"attestation_state":"computed","paper":{"title":"On reverses of the Golden-Thompson type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Bagher Ghaemi, Shigeru Furuichi, Venus Kaleibary","submitted_at":"2017-08-20T10:46:35Z","abstract_excerpt":"In this paper we present some reverses of the Golden-Thompson type inequalities:\n  Let $H$ and $K$ be Hermitian matrices such that $ e^s e^H \\preceq_{ols} e^K \\preceq_{ols} e^t e^H$ for some scalars $s \\leq t$, and $\\alpha \\in [0 , 1]$. Then for all $p>0$ and $k =1,2,\\ldots, n$ \\begin{align*} \\label{}\n  \\lambda_k (e^{(1-\\alpha)H + \\alpha K} ) \\leq (\\max \\lbrace S(e^{sp}), S(e^{tp})\\rbrace)^{\\frac{1}{p}} \\lambda_k (e^{pH} \\sharp_\\alpha e^{pK})^{\\frac{1}{p}}, \\end{align*} where $A\\sharp_\\alpha B = A^\\frac{1}{2} \\big ( A^{-\\frac{1}{2}} B^\\frac{1}{2} A^{-\\frac{1}{2}} \\big) ^\\alpha A^\\frac{1}{2}$ i"},"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":"1708.05951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-20T10:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"2a70414c89172e9db1c1ec433e6a50e2aa8c0861f64312f603e78d594e86ba07","abstract_canon_sha256":"28497b9f1813e594638eaed5ce10eff1537034f8d13f907475241683c8fca619"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:31.616278Z","signature_b64":"DFxHg69QtZ3iQZlxJnK/738hdypNpDKNJg8hX7IEb0C6XijMAbkHiIfSt+Y5R8VBBk87qx78YXX7a10cddDVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68d1b029602afb6d3bbbc08849645275371ce77384ae9e8862360a257ae30629","last_reissued_at":"2026-05-18T00:18:31.615653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:31.615653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On reverses of the Golden-Thompson type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Bagher Ghaemi, Shigeru Furuichi, Venus Kaleibary","submitted_at":"2017-08-20T10:46:35Z","abstract_excerpt":"In this paper we present some reverses of the Golden-Thompson type inequalities:\n  Let $H$ and $K$ be Hermitian matrices such that $ e^s e^H \\preceq_{ols} e^K \\preceq_{ols} e^t e^H$ for some scalars $s \\leq t$, and $\\alpha \\in [0 , 1]$. Then for all $p>0$ and $k =1,2,\\ldots, n$ \\begin{align*} \\label{}\n  \\lambda_k (e^{(1-\\alpha)H + \\alpha K} ) \\leq (\\max \\lbrace S(e^{sp}), S(e^{tp})\\rbrace)^{\\frac{1}{p}} \\lambda_k (e^{pH} \\sharp_\\alpha e^{pK})^{\\frac{1}{p}}, \\end{align*} where $A\\sharp_\\alpha B = A^\\frac{1}{2} \\big ( A^{-\\frac{1}{2}} B^\\frac{1}{2} A^{-\\frac{1}{2}} \\big) ^\\alpha A^\\frac{1}{2}$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05951","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":"1708.05951","created_at":"2026-05-18T00:18:31.615767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.05951v1","created_at":"2026-05-18T00:18:31.615767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05951","created_at":"2026-05-18T00:18:31.615767+00:00"},{"alias_kind":"pith_short_12","alias_value":"NDI3AKLAFL5W","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NDI3AKLAFL5W2O53","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NDI3AKLA","created_at":"2026-05-18T12:31:31.346846+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/NDI3AKLAFL5W2O53YCEESZCSOU","json":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU.json","graph_json":"https://pith.science/api/pith-number/NDI3AKLAFL5W2O53YCEESZCSOU/graph.json","events_json":"https://pith.science/api/pith-number/NDI3AKLAFL5W2O53YCEESZCSOU/events.json","paper":"https://pith.science/paper/NDI3AKLA"},"agent_actions":{"view_html":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU","download_json":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU.json","view_paper":"https://pith.science/paper/NDI3AKLA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.05951&json=true","fetch_graph":"https://pith.science/api/pith-number/NDI3AKLAFL5W2O53YCEESZCSOU/graph.json","fetch_events":"https://pith.science/api/pith-number/NDI3AKLAFL5W2O53YCEESZCSOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU/action/storage_attestation","attest_author":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU/action/author_attestation","sign_citation":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU/action/citation_signature","submit_replication":"https://pith.science/pith/NDI3AKLAFL5W2O53YCEESZCSOU/action/replication_record"}},"created_at":"2026-05-18T00:18:31.615767+00:00","updated_at":"2026-05-18T00:18:31.615767+00:00"}