Skip to main content
Log in

Left–Right Fredholm and Weyl Spectra of the Sum of Two Bounded Operators and Applications

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we consider the sum of two bounded linear operators defined on a Banach space and we present some new and quite general conditions to investigate their essential spectra.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abdmouleh F., Jeribi A.: Gustafson, Weidman, Kato, Wolf, Schechter, Browder, Rakoc̆ević and Schmoeger essential spectra of the sum of two bounded operators and application to a transport operator. Math. Nachr. 284, 166–176 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aiena, P.: Semi-Fredholm operators, perturbation theory and localized SVEP, XX Escuela Venezolana de Matematicas, Ed. Ivic, Merida (Venezuela) (2007)

  3. Caradus S.R.: Operators of Riesz type. Pacific J. Math. 18, 61–71 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dautray R., Lions J.L.: Analyse Mathématique et Calcul Numérique. Masson, Paris (1988)

    Google Scholar 

  5. Gohberg I., Krein I.M.G.: Fundamental theorems on deficiency numbers, root numbers and indices of linear operators. Trans. Am. Math. Soc. 2(13), 185–264 (1960)

    MathSciNet  Google Scholar 

  6. Gohberg I., Markus A., Feldman I.A.: Normally solvable operators and ideals associated with them. Trans. Am. Math. Soc 2(61), 63–84 (1967)

    Google Scholar 

  7. Goldberg S.: Unbounded Linear Operators. McGraw-Hill, New York (1966)

    MATH  Google Scholar 

  8. Greenberg W., Van Der Mee G., Protopopescu V.: Boundary Value Problems in Abstract Kinetic Theory. Birkäuser, Basel (1987)

    Book  MATH  Google Scholar 

  9. Jeribi A., Mnif M.: Fredholm operators, essential spectra and application to transport equations. Acta Appl. Math. 89, 155–176 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Jeribi A., Moalla N.: A characterization of some subsets of Schechter’s essential spectrum and application to singular transport equation. J. Math. Anal. Appl. 358(2), 434–444 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kaashoek M.A., Lay D.C.: Ascent, descent, and commuting perturbations. Trans. Am. Math. Soc. 169, 35–47 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kato T.: Perturbation theory for nullity, deficiency and other quantities of linear operators. J. Anal. Math. 6, 261–322 (1958)

    Article  MATH  Google Scholar 

  13. Latrach K.: Compactness properties for linear transport operator with abstract boundary conditions in slab geometry. Transp. Theory Stat. Phys. 22, 39–65 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Latrach K.: Time asymptotic behaviour for linear transport equation with abstract boundary conditions in slab geometry. Transp. Theory Stat. Phys. 23, 633–670 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Latrach K., Jeribi A.: Some results on Fredholm operators, essential spectra and application. J. Math. Anal. Appl. 225, 461–485 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mokhtar-Kharroubi M.: Time asymptotic behaviour and compactness in neutron transport theory. Eur. J. Mech. B Fluids 11, 39–68 (1992)

    MathSciNet  Google Scholar 

  17. Müller, V.: Spectral theory of linear operators and spectral system in Banach algebras. Oper. Theo. Adva. Appl. 139, (2003)

  18. Pelczynski, A.: On strictly singular and strictly cosingular operators. I. Strictly singular and strictly cosingular operators in \({\mathcal{C}(X)}\)-spaces. II. Strictly singular and strictly cosingular operators in L (μ)−spaces. Bull. Acad. Pol. Sci. 13, 13–36, 37–41 (1965)

    Google Scholar 

  19. Schechter M.: Principles of Functional Analysis. Acadmic Press, New York (1971)

    MATH  Google Scholar 

  20. Vladimirskii J.I.: Strictly cosingular operators. Sov. Math. Dokl. 8, 739–740 (1967)

    Google Scholar 

  21. Živković S.: Semi-Fredholm operators and perturbation. Publ. Inst. Math. Beo. 61, 73–89 (1997)

    Google Scholar 

  22. Živković-Zlatanovic̀ S., Djordjević D.S., Harte R.E.: Browder and left-right Fredholm operators. Integr. Equ. Oper. Theory 69, 347–363 (2011)

    Article  MATH  Google Scholar 

  23. Živković-Zlatanovic̀ S., Djordjević D.S., Harte R.E.: On left and right Browder operators. J. Korean Math. Soc. 485, 1053–1063 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aref Jeribi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baloudi, H., Jeribi, A. Left–Right Fredholm and Weyl Spectra of the Sum of Two Bounded Operators and Applications. Mediterr. J. Math. 11, 939–953 (2014). https://doi.org/10.1007/s00009-013-0372-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-013-0372-z

Mathematics Subject Classification (2000)

Navigation