{"paper":{"title":"Berezin number inequalities for Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Mubariz T. Karaev","submitted_at":"2018-05-02T20:58:49Z","abstract_excerpt":"In this paper, by using of the definition Berezin symbol, we show some Berezin number inequalities. Among other inequalities, it is shown that if $A, B, X\\in{\\mathbb{B}}(\\mathscr H)$, then $$\\mathbf{ber}(AX\\pm XA)\\leqslant \\mathbf{ber}^{\\frac{1}{2}}\\left(A^*A+AA^*\\right)\\mathbf{ber}^{\\frac{1}{2}}\\left(X^*X+XX^*\\right)$$ and $$\\mathbf{ber}^2(A^*XB)\\leqslant\\|X\\|^2\\mathbf{ber}(A^*A)\\mathbf{ber}(B^*B).$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01018","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"}