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Local Spectral Theory and Surjective Spectrum of Linear Relations

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Ukrainian Mathematical Journal Aims and scope

We initiate a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core K′(T) and the quasinilpotent part H0(T) of a linear relation T in a Banach space X. As an application, we present a characterization of the surjective spectrum 𝜎su(T) in terms of the local spectrum and show that if X = H0(⋋I − T) + K′(⋋I − T), then 𝜎su(T) does not cluster at ⋋.

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Authors and Affiliations

  1. University of Sfax, Sfax, Tunisia

    M. Mnif & A.-A. Ouled-Hmed

Authors
  1. M. Mnif
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  2. A.-A. Ouled-Hmed
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Correspondence to M. Mnif.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 2, pp. 222–237, February, 2021. Ukrainian DOI: 10.37863/umzh.v73i2.81.

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Mnif, M., Ouled-Hmed, AA. Local Spectral Theory and Surjective Spectrum of Linear Relations. Ukr Math J 73, 255–275 (2021). https://doi.org/10.1007/s11253-021-01920-3

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  • DOI: https://doi.org/10.1007/s11253-021-01920-3

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