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.

Full Text

Article Information

Title	L-Dunford-Pettis property in Banach spaces
Source	Methods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 387-392
MathSciNet	MR3591087
zbMATH	06742118
Milestones	Received 01/03/2016; Revised 15/04/2016
Copyright	The 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

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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