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B-essential and B-Weyl spectra of sum of two commuting bounded operators by means operator pencils

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Abstract

In this paper, we extend the work of F. Abdmouleh in Abdmouleh (Indian J. Pure Appl. Math. 47:23–31, 2016) for the operator pencils \(U-\lambda S\) where U and S two bounded linear operators acting on a Banach space X. Precisely, we define the S.B-Weyl spectrum of U and we study the S.B-Weyl spectrum of sum of two bounded linear operators acting on a Banach space.

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Authors and Affiliations

  1. Université de Sfax, Institut Supérieur de Gestion Industrielle de Sfax Route de Tunis km 10 Cité El Ons, B.P 1164-3000, Sfax, Tunisie

    Faiçal Abdmouleh

  2. Université de Sfax, Faculté des Sciences de Sfax, Sfax, Tunisie

    Kais Dhifaoui

Authors
  1. Faiçal Abdmouleh
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  2. Kais Dhifaoui
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Correspondence to Faiçal Abdmouleh.

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Communicated by Michael Kunzinger.

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Abdmouleh, F., Dhifaoui, K. B-essential and B-Weyl spectra of sum of two commuting bounded operators by means operator pencils. Monatsh Math 202, 453–464 (2023). https://doi.org/10.1007/s00605-023-01874-7

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  • DOI: https://doi.org/10.1007/s00605-023-01874-7

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