{"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"}