On some sublattices of regular operators on Banach lattices

Abstract

We give some sufficient conditions under which the linear span of positive compact (resp. Dunford-Pettis, weakly compact, AM-compact) operators cannot be a vector lattice without being a sublattice of the order complete vector lattice of all regular operators. Also, some interesting consequences are obtained.

Full Text

Article Information

Title	On some sublattices of regular operators on Banach lattices
Source	Methods Funct. Anal. Topology, Vol. 14 (2008), no. 4, 297-301
MathSciNet	MR2469068
Copyright	The Author(s) 2008 (CC BY-SA)

Authors Information

Belmesnaoui Aqzzouz
Universite Mohammed V-Souissi, Faculte des Sciences Economiques, Juridiques et Sociales, Departement d'Economie, B.P.~5295, Sala Eljadida, Morocco

Redouane Nouira
Universite Ibn Tofail, Facule des Sciences, Departement de Mathematiques, B.P.~133, Kenitra, Morocco 

Citation Example

Belmesnaoui Aqzzouz and Redouane Nouira, On some sublattices of regular operators on Banach lattices, Methods Funct. Anal. Topology 14 (2008), no. 4, 297-301.

BibTex

@article {MFAT451,
    AUTHOR = {Aqzzouz, Belmesnaoui and Nouira, Redouane},
     TITLE = {On some sublattices of regular operators on Banach  lattices},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {14},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {297-301},
      ISSN = {1029-3531},
  MRNUMBER = {MR2469068},
       URL = {http://mfat.imath.kiev.ua/article/?id=451},
}