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Birkhoff–James orthogonality and numerical radius inequalities of operator matrices

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Abstract

We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of numerical radius for \(n\times n\) operator matrices, which improve on and generalize existing lower bounds. We also obtain a better lower bound of numerical radius for an upper triangular operator matrix.

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Authors and Affiliations

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

    Arpita Mal, Kallol Paul & Jeet Sen

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  1. Arpita Mal
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  2. Kallol Paul
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  3. Jeet Sen
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Communicated by Gerald Teschl.

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Miss Arpita Mal would like to thank UGC, Govt. of India for the financial support in the form of Senior Research Fellowship under the mentorship of Prof. Kallol Paul. Mr. Jeet Sen would like to thank CSIR, Govt. of India for the financial support in the form of Senior Research Fellowship under the mentorship of Prof. Kallol Paul.

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Mal, A., Paul, K. & Sen, J. Birkhoff–James orthogonality and numerical radius inequalities of operator matrices. Monatsh Math 197, 717–731 (2022). https://doi.org/10.1007/s00605-021-01638-1

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  • DOI: https://doi.org/10.1007/s00605-021-01638-1

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