Some properties of weak Banach-Saks operators

Othman Aboutafail; Larbi Zraoula; Noufissa Hafidi

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 4, page 407-418
  • ISSN: 0862-7959

Abstract

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We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).

How to cite

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Aboutafail, Othman, Zraoula, Larbi, and Hafidi, Noufissa. "Some properties of weak Banach-Saks operators." Mathematica Bohemica 146.4 (2021): 407-418. <http://eudml.org/doc/298164>.

@article{Aboutafail2021,
abstract = {We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).},
author = {Aboutafail, Othman, Zraoula, Larbi, Hafidi, Noufissa},
journal = {Mathematica Bohemica},
keywords = {weak Banach-Saks operator; weakly compact operator; L-weakly compact operator; M-weakly compact operator; order continuous norm; positive Schur property; reflexive Banach space},
language = {eng},
number = {4},
pages = {407-418},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some properties of weak Banach-Saks operators},
url = {http://eudml.org/doc/298164},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Aboutafail, Othman
AU - Zraoula, Larbi
AU - Hafidi, Noufissa
TI - Some properties of weak Banach-Saks operators
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 4
SP - 407
EP - 418
AB - We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).
LA - eng
KW - weak Banach-Saks operator; weakly compact operator; L-weakly compact operator; M-weakly compact operator; order continuous norm; positive Schur property; reflexive Banach space
UR - http://eudml.org/doc/298164
ER -

References

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