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Norm and numerical radius inequalities for Hilbert space operators

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Abstract

In this paper, we prove some inequalities of the operator norm and the numerical radius for Hilbert spaces operators. More precisely, we prove that if \(A, B \in \mathbb {B(H)}\) and \(AB=-BA^{*}\), then

$$\begin{aligned} \omega (AB) \le D_{A} \Vert B\Vert , \end{aligned}$$

where \({{D}_{A}}=\underset{\lambda \in {\mathbb {C}}}{\mathop {\inf }}\,\left\| A-\lambda I \right\| .\)

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Acknowledgements

The authors thank the Editorial Board and the referees for their valuable comments that helped to improve the article.

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Authors and Affiliations

  1. Department of Mathematics, Safadasht Branch, Islamic Azad University, Tehran, Iran

    Baharak Moosavi

  2. Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

    Mohsen Shah Hosseini

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  1. Baharak Moosavi
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  2. Mohsen Shah Hosseini
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Correspondence to Baharak Moosavi.

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Moosavi, B., Shah Hosseini, M. Norm and numerical radius inequalities for Hilbert space operators. J Anal 31, 1393–1400 (2023). https://doi.org/10.1007/s41478-022-00521-y

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  • DOI: https://doi.org/10.1007/s41478-022-00521-y

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