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A Note on the Browder’s and Weyl’s theorem

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Abstract

Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T. In this work, we show that Browder’s theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl’s theorem for operator satisfying E(T) = π(T). An application is also given.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science Semlalia, B.O. 2390, Marrakesh, Morocco

    M. Amouch

  2. Department of Mathematics, Faculty of Science of Rabat, B. O. 1014, Rabat, Morocco

    H. Zguitti

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  1. M. Amouch
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  2. H. Zguitti
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Correspondence to M. Amouch.

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Amouch, M., Zguitti, H. A Note on the Browder’s and Weyl’s theorem. Acta. Math. Sin.-English Ser. 24, 2015–2020 (2008). https://doi.org/10.1007/s10114-008-6633-2

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  • DOI: https://doi.org/10.1007/s10114-008-6633-2

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