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Spectra for upper triangular linear relation matrices through local spectral theory

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Abstract

Let X and Y be Banach spaces. When A and B are linear relations in X and Y, respectively, we denote by \(M_{C}\) the linear relation in \(X\times Y\) of the form \(\left( \begin{array}{cc} A &{} C \\ 0 &{} B \\ \end{array} \right) \), where 0 is the zero operator from X to Y and C is a bounded operator from Y to X. In this paper, by using properties of the SVEP, we study the defect set \((\Sigma (A)\cup \Sigma (B))\backslash \Sigma (M_{C})\), where \(\Sigma \) is the spectrum, the approximate point spectrum, the surjective spectrum, the Fredholm spectrum, the Weyl spectrum, the Browder spectrum, the generalized Drazin spectrum and the Drazin spectrum.

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Authors and Affiliations

  1. Department of Mathematics, University of Oviedo, 33007, Oviedo, Asturias, Spain

    Teresa Álvarez

  2. Department of Mathematics, University of Monastir, Higher Institute of Computer Science of Mahdia, Mahdia, Tunisia

    Sonia Keskes

  3. Laboratory of Dynamic systems and Combinatorial, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia

    Sonia Keskes

Authors
  1. Teresa Álvarez
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  2. Sonia Keskes
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All authors contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript and contributed to the final manuscript.

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Correspondence to Teresa Álvarez.

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Álvarez, T., Keskes, S. Spectra for upper triangular linear relation matrices through local spectral theory. Aequat. Math. 98, 399–422 (2024). https://doi.org/10.1007/s00010-023-00993-8

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  • DOI: https://doi.org/10.1007/s00010-023-00993-8

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