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On Symmetrizable Operators on Hilbert Spaces

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Abstract

This paper, motivated by transport theory, deals with spectral properties of operators G on a complex Hilbert space H such that SG is self-adjoint where S is a nonnegative operator: We give several lower bounds of the spectral radius of G and determine the latter in some cases. We derive the whole spectrum for power compact G by means of Lagrange multiplier theory. We find out spectral connections between G and SG. We give a (spectral) stability estimate for symmetrizable operators in terms of the spectral radius of the perturbation.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences, Université d’Oran Essenia, B.P 1524 El’ M’naoueur, 31000, Oran, Algeria

    Hocine Mokhtar-Kharroubi

  2. Département de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25030, Besançon, France

    Mustapha Mokhtar-Kharroubi

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  1. Hocine Mokhtar-Kharroubi
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  2. Mustapha Mokhtar-Kharroubi
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Correspondence to Mustapha Mokhtar-Kharroubi.

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Mokhtar-Kharroubi, H., Mokhtar-Kharroubi, M. On Symmetrizable Operators on Hilbert Spaces. Acta Appl Math 102, 1–24 (2008). https://doi.org/10.1007/s10440-007-9185-z

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