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A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications

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A Correction to this article was published on 16 June 2020

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Abstract

In this paper, we aim to introduce and characterize the numerical radius orthogonality of operators on a complex Hilbert space \({\mathcal {H}}\) which are bounded with respect to the seminorm induced by a positive operator A on \({\mathcal {H}}\). Moreover, a characterization of the A-numerical radius parallelism for A-rank one operators is obtained. As applications of the results obtained, we derive some \({\mathbb {A}}\)-numerical radius inequalities of operator matrices, where \({\mathbb {A}}\) is the operator diagonal matrix whose each diagonal entry is a positive operator A on a complex Hilbert space \({\mathcal {H}}.\)

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Acknowledgements

The authors would like to express their gratitude to the referee for his/her comments towards an improved final version of the paper. 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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Authors and Affiliations

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

    Pintu Bhunia & Kallol Paul

  2. University of Sfax, Sfax, Tunisia

    Kais Feki

Authors
  1. Pintu Bhunia
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  2. Kais Feki
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  3. Kallol Paul
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Correspondence to Kais Feki.

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Communicated by Mohammad B. Asadi.

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Bhunia, P., Feki, K. & Paul, K. A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications. Bull. Iran. Math. Soc. 47, 435–457 (2021). https://doi.org/10.1007/s41980-020-00392-8

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  • DOI: https://doi.org/10.1007/s41980-020-00392-8

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