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Stability of essential B-spectra of unbounded linear operators and applications

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Abstract

In this paper, we study the stability of some essential B-spectra of closed linear operators on a Banach space X,  under polynomially finite rank operators and we give the characterization of some essential B-spectra of a \(2\times 2\) of unbounded matrix operator acting in the product of Banach spaces \(X\times Y\). Then, using the functional calculus, we prove that a spectral mapping type theorem holds for these essential B-spectra. As an application, we study the effect of the functional calculus on the class of meromorphic operators, and on the class of isoloid operators with sable sign index, satisfying generalized Weyl theorem.

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Authors and Affiliations

  1. Laboratory LAGA, Department of Mathematics, Science Faculty of Oujda, University Mohamed I, Oujda, Morocco

    Mohamed Berkani

  2. Department of Mathematics, Science Faculty of Sfax, University of Sfax, Sfax, Tunisia

    Monia Boudhief & Nedra Moalla

Authors
  1. Mohamed Berkani
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  2. Monia Boudhief
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  3. Nedra Moalla
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Correspondence to Nedra Moalla.

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Berkani, M., Boudhief, M. & Moalla, N. Stability of essential B-spectra of unbounded linear operators and applications. Afr. Mat. 29, 1189–1202 (2018). https://doi.org/10.1007/s13370-018-0609-x

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  • DOI: https://doi.org/10.1007/s13370-018-0609-x

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