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\(\varepsilon \)-Numerical Range of Operator Polynomial

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Abstract

Relying on some ideas of numerical ranges, we introduce, for operators polynomials on a complex Hilbert space, a new notion called the \(\varepsilon \)-numerical range of operators polynomials. Some geometrical and topological properties of these \(\varepsilon \)-numerical range are proved. Thereby, we achieve a new characterization of \(\varepsilon \)-numerical range of operators polynomials on an arbitrary Hilbert space. All our results are new even for \(n\times n\)-matrix polynomials.

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Authors and Affiliations

  1. Higher Institute of Applied Sciences and Technology of Sousse, University of Sousse, Sousse Ibn Khaldoun, 4003, Sousse, Tunisia

    Kamel Mahfoudhi

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  1. Kamel Mahfoudhi
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All authors reviewed the manuscript.

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Correspondence to Kamel Mahfoudhi.

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Communicated by Izchak Lewkowicz.

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Mahfoudhi, K. \(\varepsilon \)-Numerical Range of Operator Polynomial. Complex Anal. Oper. Theory 18, 41 (2024). https://doi.org/10.1007/s11785-024-01485-6

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  • DOI: https://doi.org/10.1007/s11785-024-01485-6

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