Skip to main content
SpringerLink
Log in

On the class of semi-weakly compact operators

  • Published:
Rendiconti del Circolo Matematico di Palermo Series 2 Aims and scope Submit manuscript

Abstract

Our objective in this paper is to continue the investigation of the duality problem for the class of AWC operators. First, we introduce a new class of operators called semi weakly compact operators and we study the basic properties of this class. Also, we shall give some relations between almost weakly compact and semi weakly compact operators through the use of the adjoint. Finally, we will give a condition under which if the adjoint \(T'\) is AWC,  then so is T.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data Availability Statement

No data were used to support this study.

References

  1. Aliprantis, C.D., Burkinshaw, O.: Positive operators. Springer, Cham (2006)

    Book  MATH  Google Scholar 

  2. Aiena, P.: Fredholm and local spectral theory, with applications to multipliers. Kluwer Academic, Dordrecht (2004)

    MATH  Google Scholar 

  3. Goldberg, S., Thorp, E.: On some open questions concerning strictly singular operators. Proc. Am. Math. Soc. 14, 334–336 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fabian, M., Habala, P., Hajek, P., Montesinos, V., Zizler, V.: Banach space theory. The basis for linear and nonlinear analysis. Springer, New York (2011)

    Book  MATH  Google Scholar 

  5. Baklouti, H., Hajji, M.: Domination problem on Banach lattices and almost weak compactness. Positivity. 19, 797–805 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Herman, R.H.: Generalization of weakly compact operator. Trans. Am. Math. Soc. 13, 377–386 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  7. Howard, J.: A generalization of reflexive Banach spaces and weakly compact operators. Comment. Math. Univ. Carolinae 13, 673–684 (1972)

    MathSciNet  MATH  Google Scholar 

  8. Kato, T.: Perturbation theory for nullity deficiency and other quantities of linear operators. J. Analyse Math. 6, 273–322 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces I. Sequence spaces. Springer-Verlag, New-York (1977)

    MATH  Google Scholar 

  10. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Function spaces. Springer-Verlag, New-York (1979)

    Book  MATH  Google Scholar 

  11. Meyer-Niberg, P.: Banach lattice. Springer, Berlin (1991)

    Book  Google Scholar 

  12. Megginson, R.E.: An introduction to banach space theory. Springer-Verlag, New York (1990)

    MATH  Google Scholar 

  13. Pelczynski, A.: On strictly singular and strictly cosingular operators. Bull. Acad. Pol. Sci. 8, 31–41 (1965)

    MathSciNet  MATH  Google Scholar 

  14. Whitley, R.J.: Strictly singular operators and their conjugates. Trans. Am. Math. Soc. 113, 252–261 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wójtowicz, M.: The lattice copies of \(l_1\) in Banach lattices. Comment. Math. Univ. Carolin. 42(4), 649–653 (2001)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Issat Kasserine, BP 471, 1200, Kasserine, Tunisia

    Mohamed Hajji

Authors
  1. Mohamed Hajji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Hajji.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hajji, M. On the class of semi-weakly compact operators. Rend. Circ. Mat. Palermo, II. Ser 72, 1315–1323 (2023). https://doi.org/10.1007/s12215-022-00734-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-022-00734-x

Keywords

Mathematics Subject Classification

Search

Navigation