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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","authors_text":"Mohammad Bagher Ghaemi, Shigeru Furuichi, Venus Kaleibary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-20T10:46:35Z","title":"On reverses of the Golden-Thompson type inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05951","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7f58e975507d3b5bf5738aad2893cd51cae159c0e20f2e320c9e0a2fbbd60711","target":"record","created_at":"2026-05-18T00:18:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"28497b9f1813e594638eaed5ce10eff1537034f8d13f907475241683c8fca619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-20T10:46:35Z","title_canon_sha256":"2a70414c89172e9db1c1ec433e6a50e2aa8c0861f64312f603e78d594e86ba07"},"schema_version":"1.0","source":{"id":"1708.05951","kind":"arxiv","version":1}},"canonical_sha256":"68d1b029602afb6d3bbbc08849645275371ce77384ae9e8862360a257ae30629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68d1b029602afb6d3bbbc08849645275371ce77384ae9e8862360a257ae30629","first_computed_at":"2026-05-18T00:18:31.615653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:31.615653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DFxHg69QtZ3iQZlxJnK/738hdypNpDKNJg8hX7IEb0C6XijMAbkHiIfSt+Y5R8VBBk87qx78YXX7a10cddDVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:31.616278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f58e975507d3b5bf5738aad2893cd51cae159c0e20f2e320c9e0a2fbbd60711","sha256:b9a0a0e5a38331b8541462d4693541a021612374d01604361df3b6b06f8df1cc"],"state_sha256":"7345cbbb326eb6a3f2a6c3fa872c2b89dfcb6b688387ae4f461bf269d632eb93"}