Abstract
We present sharp lower bounds for the A-numerical radius of semi-Hilbertian space operators. We also present an upper bound. Further we compute new upper bounds for the B-numerical radius of \(2 \times 2\) operator matrices where \(B = \textit{diag}(A,A)\), A being a positive operator. As an application of the A-numerical radius inequalities, we obtain a bound for the zeros of a polynomial which is quite a bit improvement of some famous existing bounds for the zeros of polynomials.
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Acknowledgements
The authors would like to thank the referees for their insightful suggestions that helped us to improve this article. Pintu Bhunia and Raj Kumar Nayak would like to thank UGC, Govt. of India for the financial support in the form of senior research fellowship. Prof. Kallol Paul would like to thank RUSA 2.0, Jadavpur University for the partial support.
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Communicated by Qingxiang Xu.
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Bhunia, P., Nayak, R.K. & Paul, K. Refinements of A-numerical radius inequalities and their applications. Adv. Oper. Theory 5, 1498–1511 (2020). https://doi.org/10.1007/s43036-020-00056-8
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DOI: https://doi.org/10.1007/s43036-020-00056-8