Czechoslovak Mathematical Journal

, Volume 59, Issue 3, pp 827–834 | Cite as

The order σ-complete vector lattice of AM-compact operators

  • Belmesnaoui Aqzzouz
  • Redouane Nouira


We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice E into a Banach lattice F is an order σ-complete vector lattice.


AM-compact operator order continuous norm discrete vector lattice 

MSC 2000

46A40 46B40 46B42 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. A. Abramovich and A. W. Wickstead: Solutions of several problems in the theory of compact positive operators. Proc. Amer. Math. Soc. 123 (1995), 3021–3026.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    C. D. Aliprantis and O. Burkinshaw: Locally solid Riesz spaces. Academic Press, 1978.Google Scholar
  3. [3]
    C. D. Aliprantis and O. Burkinshaw: Positive compact operators on Banach lattices. Math. Z. 174 (1980), 289–298.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    C. D. Aliprantis and O. Burkinshaw: On weakly compact operators on Banach lattices. Proc. Amer. Math. Soc. 83 (1981), 573–578.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    B. Aqzzouz and R. Nouira: Les opérateurs précompacts sur les treillis vectoriels localement convexes-solides. Sci. Math. Jpn. 57 (2003), 279–256.MATHMathSciNetGoogle Scholar
  6. [6]
    Z. L. Chen and A. W. Wickstead: Vector lattices of weakly compact operators on Banach lattices. Trans. Amer. Math. Soc. 352 (1999), 397–412.CrossRefMathSciNetGoogle Scholar
  7. [7]
    D. H. Fremlin: Riesz spaces with the order continuity property I. Proc. Cambr. Phil. Soc. 81 (1977), 31–42.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    U. Krengel: Remark on the modulus of compact operators. Bull. Amer. Math. Soc. 72 (1966), 132–133.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    P. Meyer-Nieberg: Banach lattices. Universitext. Springer-Verlag, Berlin, 1991.Google Scholar
  10. [10]
    A. P. Robertson and W. Robertson: Topological vector spaces. 2nd ed., Cambridge University Press, London, 1973.MATHGoogle Scholar
  11. [11]
    A. W. Wickstead: Dedekind completeness of some lattices of compact operators. Bull. Polish Acad. of Sci. Math. 43 (1995), 297–304.MATHMathSciNetGoogle Scholar
  12. [12]
    A. W. Wickstead: Converses for the Dodds-Fremlin and Kalton-Saab theorems. Math. Proc. Camb. Phil. Soc. 120 (1996), 175–179.MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    A. C. Zaanen: Riesz spaces II. North Holland Publishing Company, 1983.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Faculté des Sciences Economiques, Juridiques et Sociales, Département d’EconomieUniversité Mohammed V-SouissiSala EljadidaMorocco

Personalised recommendations