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Some A-spectral radius inequalities for A-bounded Hilbert space operators

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Abstract

Let \(r_A(T)\) denote the A-spectral radius of an operator T which is bounded with respect to the seminorm induced by a positive operator A on a complex Hilbert space \({\mathcal {H}}\). In this paper, we aim to establish several A-spectral radius inequalities for products, sums and commutators of A-bounded operators. Some applications of our results are provided. Moreover, we give an affirmative answer to the question recently posed by Baklouti and Namouri (Banach J Math Anal 16:12, https://doi.org/10.1007/s43037-021-00167-1, 2022) regarding the connection between the notions of A-spectral radius and A-spectrum for A-bounded operators.

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Acknowledgements

The author would like to express his gratitude to the editor and the anonymous referees for their comments towards an improved final version of the paper.

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Authors and Affiliations

  1. Faculty of Economic Sciences and Management of Mahdia, University of Monastir, Mahdia, Tunisia

    Kais Feki

  2. Laboratory Physics-Mathematics and Applications (LR/13/ES-22), Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia

    Kais Feki

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  1. Kais Feki
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Correspondence to Kais Feki.

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Communicated by Esteban Andruchow.

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Feki, K. Some A-spectral radius inequalities for A-bounded Hilbert space operators. Banach J. Math. Anal. 16, 31 (2022). https://doi.org/10.1007/s43037-022-00185-7

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  • DOI: https://doi.org/10.1007/s43037-022-00185-7

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