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New upper bounds for the numerical radius of operators on Hilbert spaces

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Abstract

This article presents some refinements and generalizations of existing numerical radius inequalities for Hilbert space operators. Further, several upper bounds for numerical radius with the Cartesian decomposition of an operator are provided. Also, we prove various upper bounds for the numerical radius of diagonal and off-diagonal operator matrices. Additionally, we establish certain numerical radius inequalities for operators using quadratic weighted operator geometric mean.

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Acknowledgements

The authors thank the referee and the editor for the valuable suggestions and comments on an earlier version. Incorporating appropriate responses to these in the article has led to a better presentation of the results.

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Authors and Affiliations

  1. School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, India

    Satyajit Sahoo

  2. Department of Mathematics, National Institute of Technology Raipur, Raipur, 492010, India

    Nirmal Chandra Rout

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  1. Satyajit Sahoo
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  2. Nirmal Chandra Rout
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Correspondence to Nirmal Chandra Rout.

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Communicated by Mario Krnic.

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Sahoo, S., Rout, N.C. New upper bounds for the numerical radius of operators on Hilbert spaces. Adv. Oper. Theory 7, 50 (2022). https://doi.org/10.1007/s43036-022-00216-y

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