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Finite Rank and Small Perturbations of Linear Relations

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Abstract

In this paper, we investigate the stability of regular, semi-Fredholm, finite essential ascent and finite essential descent linear relations under small and commuting finite rank perturbations as well as the behavior of the nullity, the defect and the index under such perturbations.

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References

  1. Chafai, E., Mnif, M.: Spectral mapping theorem for ascent, essential ascent, descent and essential descent spectrum of linear relations. Acta Math. Sci. 34B(4), 1212–1224 (2014)

    Article  MathSciNet  Google Scholar 

  2. Aiena, P.: Fredholm and Local Spectral Theory with Application to Multipliers. Kluwer Academic, Dordrecht (2004)

    MATH  Google Scholar 

  3. Fredj, O.B.H., Burgos, M., Oudghiri, M.: Ascent spectrum and essential ascent spectrum. Stud. Math. 187(1), 59–73 (2008)

    Article  MathSciNet  Google Scholar 

  4. Fredj, O.B.H.: Essential descent spectrum and compact commuting perturbations. Extracta Mathematicae 21(3), 261–271 (2006)

    MathSciNet  MATH  Google Scholar 

  5. Baskakov, A.G., Chernyshov, K.I.: Spectral analysis of linear relations and degenerate operator semigroups. Mat. Sb. 193, 1573–1610 (2003)

    Article  Google Scholar 

  6. Favini, A., Yagi, A.: Degenerate Differential Equations in Banach Spaces. Marcel Dekker, New York (1999)

    MATH  Google Scholar 

  7. Derkach, V.A., Hassi, S., Malamud, M.M., Snoo, H.S.V.: Boundary relations and their Weyl families. Trans. Am. Math. Soc. 358, 5351–5400 (2006)

    Article  MathSciNet  Google Scholar 

  8. Kaczynski, T.: Multivalued maps as a tool in modeling and rigorous numerics. J. Fixed Point Theory Appl. 4, 151–176 (2008)

    Article  MathSciNet  Google Scholar 

  9. Sandovici, A., Snoo, H.: An index for the product of linear relations. Linear Algebra Appl. 431, 2160–2171 (2009)

    Article  MathSciNet  Google Scholar 

  10. Cross, R.W.: Multivalued Linear Operators. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  11. Sandovici, A., Snoo, H., Winkler, H.: Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces. Linear Algebra Appl. 423, 456–497 (2007)

    Article  MathSciNet  Google Scholar 

  12. Fakhfakh, F., Mnif, M.: Perturbation theory of lower semi-Browder multivalued linear operators. Publ. Math. Debrecen 78(3–4), 595–606 (2011)

    Article  MathSciNet  Google Scholar 

  13. Labrousse, JPh, Sandovici, A., Snoo, H.S.V., Winkler, H.: The Kato decomposition of quasi-Fredholm relations. Oper. Matrices 4, 1–51 (2010)

    Article  MathSciNet  Google Scholar 

  14. Jaftha, J.J.: The conjugate of a product of linear relations. Comment. Math. Univ. Carol. 47(2), 265–273 (2006)

    MathSciNet  MATH  Google Scholar 

  15. Álvarez, T.: On regular linear relations. Acta Math. Sin. 28(1), 183–194 (2012)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The work of Teresa Álvarez was supported by Micinn (Spain). Grant MTM 2013-45643.

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Author notes

  1. Ezzeddine Chafai

    Present address: Department of Mathematics, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, 3018, Sfax, Tunisia

    Ezzeddine Chafai

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

    Teresa Álvarez

Authors
  1. Ezzeddine Chafai
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  2. Teresa Álvarez
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Correspondence to Ezzeddine Chafai.

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Chafai, E., Álvarez, T. Finite Rank and Small Perturbations of Linear Relations. Mediterr. J. Math. 15, 202 (2018). https://doi.org/10.1007/s00009-018-1247-0

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  • DOI: https://doi.org/10.1007/s00009-018-1247-0

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