Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 599 - 607 2020-04-02

Almost L-Dunford-Pettis sets in Banach lattices and its applications

Abderrahman RETBI [1]


We introduce and study the notion of almost L-Dunford-Pettis sets in Banach lattices and we give some characterizations of it in terms of sequences. As an application, we establish new properties of almost Dunford-Pettis completely continuous operators. Finally, by introducing the concept of aL-Dunford-Pettis property in Banach lattices, we investigate the weak compactness of almost Dunford-Pettis completely continuous operator.
Banach lattice, Dunford-Pettis set, relatively compact Dunford-Pettis property, Dunford-Pettis completely continuous operator
  • [1] C.D. Aliprantis and O. Burkinshaw, Positive operators, Reprint of the 1985 original. Springer, Dordrecht, 2006.
  • [2] K.T. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241, 35-41, 1979.
  • [3] K. Bouras, Almost Dunford-Pettis sets in Banach lattices, Rend. Circ. Mat. Palermo. 62, 227-236, 2013.
  • [4] K. El Fahri, N. Machrafi and M. Moussa, Banach Lattices with the Positive Dunford- Pettis Relatively Compact Property, Extracta Math. 30 (2), 161-179, 2015.
  • [5] P. Meyer-Nieberg, Banach lattices, Universitext, Springer-Verlag, Berlin, 1991.
  • [6] A. Retbi and B. El Wahbi, L-Dunford-Pettis property in Banach spaces, Methods Funct. Anal. Topology, accepted.
  • [7] Y. Wen and J. Chen, Characterizations of Banach Spaces With Relatively Compact Dunford-Pettis Sets, Advances in Mathematics (China), 45 (1), 122-132, 2016.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0002-0868-1563
Yazar: Abderrahman RETBI (Sorumlu Yazar)
Kurum: Ibn Tofail University
Ülke: Morocco


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms568386, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {599 - 607}, doi = {10.15672/hujms.568386}, title = {Almost L-Dunford-Pettis sets in Banach lattices and its applications}, key = {cite}, author = {RETBI, Abderrahman} }
APA RETBI, A . (2020). Almost L-Dunford-Pettis sets in Banach lattices and its applications. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 599-607 . DOI: 10.15672/hujms.568386
MLA RETBI, A . "Almost L-Dunford-Pettis sets in Banach lattices and its applications". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 599-607 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/568386>
Chicago RETBI, A . "Almost L-Dunford-Pettis sets in Banach lattices and its applications". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 599-607
RIS TY - JOUR T1 - Almost L-Dunford-Pettis sets in Banach lattices and its applications AU - Abderrahman RETBI Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.568386 DO - 10.15672/hujms.568386 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 599 EP - 607 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.568386 UR - https://doi.org/10.15672/hujms.568386 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Almost L-Dunford-Pettis sets in Banach lattices and its applications %A Abderrahman RETBI %T Almost L-Dunford-Pettis sets in Banach lattices and its applications %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.568386 %U 10.15672/hujms.568386
ISNAD RETBI, Abderrahman . "Almost L-Dunford-Pettis sets in Banach lattices and its applications". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 599-607 . https://doi.org/10.15672/hujms.568386
AMA RETBI A . Almost L-Dunford-Pettis sets in Banach lattices and its applications. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 599-607.
Vancouver RETBI A . Almost L-Dunford-Pettis sets in Banach lattices and its applications. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 607-599.