{"paper":{"title":"Improvements of Berezin number inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour","submitted_at":"2018-05-08T19:02:20Z","abstract_excerpt":"In this paper, we generalize several Berezin number inequalities involving product of operators. For instance, we show that if $A, B$ are positive operators and $X$ is any operator, then \\begin{align*} \\textbf{ber}^{r}(H_{\\alpha}(A,B))&\\leq\\frac{\\|X\\|^{r}}{2}\\textbf{ber}(A^{r}+B^{r})&\\leq\\frac{\\|X\\|^{r}}{2}\\textbf{ber}(\\alpha A^{r}+(1-\\alpha)B^{r})+\\textbf{ber}((1-\\alpha)A^{r}+\\alpha B^{r}), \\end{align*} where $H_{\\alpha}(A,B)=\\frac{A^\\alpha XB^{1-\\alpha}+A^{1-\\alpha} XB^{\\alpha}}{2}$, $0\\leq\\alpha\\leq1$ and $r\\geq2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03231","kind":"arxiv","version":2},"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"}