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Some Upper Bounds for the Davis–Wielandt Radius of Hilbert Space Operators

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Abstract

In this paper, we give several inequalities involving the Davis–Wielandt radius and the numerical radii of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then

$$\begin{aligned} dw(T) \le \Big (w\big (|T|^4 + |T|^8\big ) + 2w^2\big (|T|^2T\big )\Big )^{\frac{1}{4}}, \end{aligned}$$

where \(dw(\cdot )\) and \(w(\cdot )\) are the Davis–Wielandt radius and the numerical radius, respectively.

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Acknowledgements

The authors would like to sincerely thank the referee for her/his valuable suggestions and comments. The first named author (corresponding author) was supported by a grant from Shanghai Municipal Science and Technology Commission (18590745200).

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Authors and Affiliations

  1. Department of Mathematics, Farhangian University, Tehran, Iran

    Ali Zamani

  2. Department of Mathematics, Al-Balqa Applied University, Salt, Jordan

    Khalid Shebrawi

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  1. Ali Zamani
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  2. Khalid Shebrawi
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Correspondence to Ali Zamani.

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Zamani, A., Shebrawi, K. Some Upper Bounds for the Davis–Wielandt Radius of Hilbert Space Operators. Mediterr. J. Math. 17, 25 (2020). https://doi.org/10.1007/s00009-019-1458-z

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  • DOI: https://doi.org/10.1007/s00009-019-1458-z

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