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Improvement of A-Numerical Radius Inequalities of Semi-Hilbertian Space Operators

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Abstract

Let \(\mathcal {H}\) be a complex Hilbert space and let A be a positive operator on \(\mathcal {H}\). We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian space \(\mathcal {B}_A(\mathcal {H})\) that generalize and improve on the existing ones. Further, we estimate an upper bound for the \(\mathbb {A}\)-operator seminorm of \(2\times 2\) operator matrices, where \(\mathbb {A}=\text{ diag }(A,A)\). The bound obtained here generalizes the earlier related bound.

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Acknowledgements

Pintu Bhunia and Raj Kumar Nayak 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. We would like to thank the referee for their valuable suggestions.

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

    Pintu Bhunia, Raj Kumar Nayak & Kallol Paul

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  1. Pintu Bhunia
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  2. Raj Kumar Nayak
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  3. Kallol Paul
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Correspondence to Kallol Paul.

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Bhunia, P., Nayak, R.K. & Paul, K. Improvement of A-Numerical Radius Inequalities of Semi-Hilbertian Space Operators. Results Math 76, 120 (2021). https://doi.org/10.1007/s00025-021-01439-w

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