Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals

  • Halimeh ArdakaniEmail author
  • Manijeh Salimi
  • Seyed Mohammad Moshtaghioun
Original Paper


By introducing the concepts of strongly limited completely continuous and strongly Dunford–Pettis completely continuous subspaces of operator ideals, it will be given some characterizations of these concepts in terms of lcc ness and DPcc ness of all their evaluation operators related to that subspace. In particular, when \(X^*\) or Y has the Gelfand–Phillips (GP) property, we give a characterization of GP property of a closed subspace \({\mathcal {M}}\) of compact operators K(XY) in terms of strong limited complete continuity of \({\mathcal {M}}\). Also it is shown that, each operator ideal \({\mathcal {U}}(X, Y )\) is strongly limited completely continuous, iff, \(X^*\) and Y have the GP property.


Gelfand–Phillips property Completely continuous algebra Strongly completely continuous algebra Limited completely continuous operator 

Mathematics Subject Classification

47L05 47L20 46B28 46B99 


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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  • Halimeh Ardakani
    • 1
    Email author
  • Manijeh Salimi
    • 2
  • Seyed Mohammad Moshtaghioun
    • 3
  1. 1.Department of MathematicsPayame Noor UniversityTehranIran
  2. 2.Department of MathematicsFarhangian UniversityTehranIran
  3. 3.Department of MathematicsYazd UniversityYazdIran

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