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L-Dunford-Pettis property in Banach spaces


Abstract

In this paper, we introduce and study the concept of L-Dunford-Pettis sets and L-Dunford-Pettis property in Banach spaces. Next, we give a characterization of the L-Dunford-Pettis property with respect to some well-known geometric properties of Banach spaces. Finally, some complementability of operators on Banach spaces with the L-Dunford-Pettis property are also investigated.

Key words: Dunford-Pettis set, Dunford-Pettis relatively compact property, Dunford-Pettis completely continuous operator.


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Article Information

TitleL-Dunford-Pettis property in Banach spaces
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 387-392
MathSciNet MR3591087
zbMATH 06742118
MilestonesReceived 01/03/2016; Revised 15/04/2016
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

A. Retbi
Universite Ibn Tofail, Faculte des Sciences, Departement de Mathematiques, B.P. 133, Kenitra, Morocco

B. El Wahbi
Universite Ibn Tofail, Faculte des Sciences, Departement de Mathematiques, B.P. 133, Kenitra, Morocco


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Citation Example

A. Retbi and B. El Wahbi, L-Dunford-Pettis property in Banach spaces, Methods Funct. Anal. Topology 22 (2016), no. 4, 387-392.


BibTex

@article {MFAT916,
    AUTHOR = {Retbi, A. and El Wahbi, B.},
     TITLE = {L-Dunford-Pettis property in Banach spaces},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {387-392},
      ISSN = {1029-3531},
  MRNUMBER = {MR3591087},
 ZBLNUMBER = {06742118},
       URL = {http://mfat.imath.kiev.ua/article/?id=916},
}


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