Skip to main content
Log in

On the weak compactness of b-weakly compact operators

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

We characterize Banach lattices on which the class of b-weakly compact operators coincides with that of weakly compact operators.

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. Aliprantis C.D., Burkinshaw O.: Positive Operators. Reprint of the 1985 original. Springer, Dordrecht (2006)

    MATH  Google Scholar 

  2. Alpay S., Altin B., Tonyali C.: On property (b) of vector lattices. Positivity 7(1–2), 135–139 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alpay, S., Altin, B., Tonyali, C.: A note on Riesz spaces with property-b. Czechoslov. Math. J. 56(131), no. 2, 765–772 (2006)

    Google Scholar 

  4. Alpay S., Altin B.: A note on b-weakly compact operators. Positivity 11(4), 575–582 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Alpay S., Ercan Z.: Characterizations of Riesz spaces with b-property. Positivity 13(1), 21–30 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Altin B.: Some properties of b-weakly compact operators. G.U. J. Sci. 18(3), 391–395 (2005)

    Google Scholar 

  7. Altin B.: On b-weakly compact operators on Banach lattices. Taiwan. J. Math. 11, 143–150 (2007)

    MATH  MathSciNet  Google Scholar 

  8. Aqzzouz, B., Elbour, A., Hmichane, J.: The duality problem for the class of b-weakly compact operators. Positivity (in press)

  9. Meyer-Nieberg P.: Banach Lattices. Springer, Berlin (1991)

    MATH  Google Scholar 

  10. Schaefer H.H.: Banach Lattices and Positive Operators. Springer, Berlin (1974)

    MATH  Google Scholar 

  11. Zaanen A.C.: Riesz spaces II. North Holland Publishing Company, Amsterdam (1983)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Belmesnaoui Aqzzouz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aqzzouz, B., Elbour, A. On the weak compactness of b-weakly compact operators. Positivity 14, 75–81 (2010). https://doi.org/10.1007/s11117-009-0006-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11117-009-0006-7

Keywords

Mathematics Subject Classification (2000)

Navigation