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arXiv · 1805.01018

Berezin number inequalities for Hilbert space operators

Mojtaba Bakherad·Mubariz T. Karaev
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Abstract

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 $$\mathbf{ber}^2(A^*XB)\leqslant\|X\|^2\mathbf{ber}(A^*A)\mathbf{ber}(B^*B).$$

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Mojtaba Bakherad, Mubariz T. Karaev. 2018-05-02. Berezin number inequalities for Hilbert space operators. https://arxiv.org/abs/1805.01018

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