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Norm and numerical radius inequalities for sum of operators

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Abstract

In this paper, we present several numerical radius and norm inequalities for sum of Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator T ∈ B(H), we prove that

$$ {\omega}^{2} \left( T \right) \le \frac{1}{2}\omega \left( {T^{2} } \right) + \frac{1}{{2\sqrt 2 }}\omega \left( {\left| T \right|^{2} + i\left| {T^{\ast} } \right|^{2} } \right) .$$

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Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions which improved the paper considerably.

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  1. Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran

    Ali Zand Vakili & Ali Farokhinia

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  1. Ali Zand Vakili
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  2. Ali Farokhinia
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Correspondence to Ali Farokhinia.

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Zand Vakili, A., Farokhinia, A. Norm and numerical radius inequalities for sum of operators. Boll Unione Mat Ital 14, 647–657 (2021). https://doi.org/10.1007/s40574-021-00289-2

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  • DOI: https://doi.org/10.1007/s40574-021-00289-2

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