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Proper Improvement of Well-Known Numerical Radius Inequalities and Their Applications

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Abstract

New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space \({\mathcal {H}}\) are given. In particular, it is established that if T is a bounded linear operator on a Hilbert space \({\mathcal {H}}\) then

$$\begin{aligned} w^2(T)\le \min _{0\le \alpha \le 1} \left\| \alpha T^*T +(1-\alpha )TT^* \right\| , \end{aligned}$$

where w(T) is the numerical radius of T. The inequalities obtained here are non-trivial improvement of the well-known numerical radius inequalities. As an application we estimate bounds for the zeros of a complex monic polynomial.

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  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India

    Pintu Bhunia & Kallol Paul

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  1. Pintu Bhunia
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  2. Kallol Paul
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Correspondence to Kallol Paul.

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First author would like to thank UGC, Govt. of India for the financial support in the form of SRF. Prof. Kallol Paul would like to thank RUSA 2.0, Jadavpur University for the partial support.

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Bhunia, P., Paul, K. Proper Improvement of Well-Known Numerical Radius Inequalities and Their Applications. Results Math 76, 177 (2021). https://doi.org/10.1007/s00025-021-01478-3

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