Bounds for zeros of a polynomial using numerical radius of Hilbert space operators

Abstract

We obtain bounds for the numerical radius of \(2 \times 2\) operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here, we estimate the bounds for the zeros of a monic polynomial and illustrate with numerical examples that the bounds are better than the existing ones.

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Acknowledgements

We would like to thank the referee for his/her helpful suggestions. Mr. Pintu Bhunia 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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Correspondence to Kallol Paul.

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Communicated by Hugo Woerdeman.

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Bhunia, P., Bag, S. & Paul, K. Bounds for zeros of a polynomial using numerical radius of Hilbert space operators. Ann. Funct. Anal. 12, 21 (2021). https://doi.org/10.1007/s43034-020-00107-4

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Keywords

  • Numerical radius
  • Operator matrix
  • Zeros of polynomial

Mathematics Subject Classification

  • 47A12
  • 15A60
  • 26C10