Rendiconti del Circolo Matematico di Palermo

, Volume 59, Issue 1, pp 101–105 | Cite as

L- and M-weak compactness of positive semi-compact operators

Article

Abstract

We present some necessary and sufficient conditions for positive semi-compact operators being L-weakly compact and M-weakly compact respectively.

Keywords

Banach lattices Semi-compact operator M-weakly compact operator L-weakly compact operator 

Mathematics Subject Classification (2000)

46B42 47B07 47B60 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aliprantis, C.D., Burkinshaw, O.: Positive Operators. New York: Academic Press (1985)MATHGoogle Scholar
  2. 2.
    Aqzzouz, B., Elbour, A.: Characterization of the order weak compactness of semi-compact operators, J. Math. Anal. Appl., 355(2) (2009), 541–547MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Aqzzouz, B., Elbour, A., Hmichane, J.: The duality problem for the class of b-weakly compact operators, Positivity, 13(4) (2009), 683–692MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Aqzzouz, B., Elbour, A., Hmichane, J.: Some properties of the class of positive Dunford-Pettis operators, J. Math. Anal. Appl., 354(1) (2009), 295–300MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chen, Z.L., Wickstead, A. W.: L-weakly and M-weakly compact operators, Indag. Math. (N.S), 10(3) (1999), 321–336MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Groenewegen, G., Meyer-Nieberg, P.: An elementary and unified approach to disjoint sequence theorems,Nederl. Akad.Wetensch. Indag. Math., 48(3) (1986), 313–317MATHMathSciNetGoogle Scholar
  7. 7.
    Luxemburg, W.A.J., Zaanen, A.C.: Riesz spaces I. Amsterdam London: North Holland (1971)MATHGoogle Scholar
  8. 8.
    Meyer-Nieberg, P.: Banach Lattices. Berlin, Heideberg,New York: SpringerVerlag (1991)MATHGoogle Scholar
  9. 9.
    Wickstead, A.W.: Conversesfor theDodds-Freminand Kalton-Saab Theorems, Math. Proc. Cambridge Philos. Soc., 120 (1996), 175–179MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Italia 2010

Authors and Affiliations

  1. 1.School of MathematicsSouthwest Jiaotong UniversityChengdu, SichuanP. R. China

Personalised recommendations