{"paper":{"title":"Some extensions of the operator entropy type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Morassaei, Mojtaba Bakherad","submitted_at":"2017-04-07T13:04:56Z","abstract_excerpt":"In this paper, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond-Pe\\v{c}ari\\'c method. In particular, we present {\\tiny \\begin{align*} f&\\left[\\int_T(A_s\\natural_{p+1}B_s)d\\mu(s)+t_0\\left(I_{\\mathscr H}-\\int_TA_s\\natural_pB_sd\\mu(s)\\right)\\right]-\\gamma_ff(t_0)\\left(I_{\\mathscr H}-\\int_TA_s\\natural_pB_sd\\mu(s)\\right)\\nonumber\\\\ &\\le \\gamma_f\\widetilde{S}_p^f(\\mathbf{A}|\\mathbf{B})\\,, \\end{align*}} where $T$ is a locally compact Hausdorff space and $\\mu$ is a Radon measure on $T$, $0<m A_s \\leq B_s \\leq M A_s\\,\\,(s\\in T)$ for some positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02214","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"}