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arXiv · 2207.01007

Numerical radius and Berezin number inequality

Satyabrata Majee·Amit Maji·Atanu Manna
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Abstract

We study various inequalities for numerical radius and Berezin number of a bounded linear operator on a Hilbert space. It is proved that the numerical radius of a pure two-isometry is 1 and the Crawford number of a pure two-isometry is 0. In particular, we show that for any scalar-valuednon-constant inner function $\theta$, the numerical radius and the Crawford number of a Toeplitz operator $T_{\theta}$ on a Hardy space is 1 and 0, respectively. It is also shown that numerical radius is multiplicative for a class of isometries and sub-multiplicative for a class of commutants of a shift. We have illustrated these results with some concrete examples. Finally, some Hardy-type inequalities for Berezin number of certain class of operators are established with the help of the classical Hardy's inequality.

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Satyabrata Majee, Amit Maji, Atanu Manna. 2022-07-03. Numerical radius and Berezin number inequality. https://arxiv.org/abs/2207.01007

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