Some characterizations of weakly compact operator on Banach lattices

Belmesnaoui Aqzzouz; Khalid Bouras

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 901-908
  • ISSN: 0011-4642

Abstract

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We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.

How to cite

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Aqzzouz, Belmesnaoui, and Bouras, Khalid. "Some characterizations of weakly compact operator on Banach lattices." Czechoslovak Mathematical Journal 61.4 (2011): 901-908. <http://eudml.org/doc/196644>.

@article{Aqzzouz2011,
abstract = {We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.},
author = {Aqzzouz, Belmesnaoui, Bouras, Khalid},
journal = {Czechoslovak Mathematical Journal},
keywords = {weakly compact operator; order continuous norm; KB-space; weakly compact operator; order continuous norm; KB-space},
language = {eng},
number = {4},
pages = {901-908},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some characterizations of weakly compact operator on Banach lattices},
url = {http://eudml.org/doc/196644},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Aqzzouz, Belmesnaoui
AU - Bouras, Khalid
TI - Some characterizations of weakly compact operator on Banach lattices
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 901
EP - 908
AB - We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.
LA - eng
KW - weakly compact operator; order continuous norm; KB-space; weakly compact operator; order continuous norm; KB-space
UR - http://eudml.org/doc/196644
ER -

References

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  1. Aliprantis, Ch. D., Burkinshaw, O., Positive Operators, Reprint of the 1985 original. Springer, Berlin (2006). (2006) Zbl1098.47001MR2262133
  2. Aqzzouz, B., Nouira, R., Zraoula, L., 10.1016/j.jmaa.2005.10.083, J. Math. Anal. Appl. 324 (2006), 49-59. (2006) Zbl1112.47028MR2262455DOI10.1016/j.jmaa.2005.10.083
  3. Aqzzouz, B., Elbour, A., 10.1007/s11117-009-0006-7, Positivity 14 (2010), 75-81. (2010) Zbl1198.47034MR2596465DOI10.1007/s11117-009-0006-7
  4. Aqzzouz, B., Elbour, A., Hmichane, J., 10.1016/j.jmaa.2008.12.063, J. Math. Anal. Appl. 354 (2009), 295-300. (2009) Zbl1167.47033MR2510440DOI10.1016/j.jmaa.2008.12.063
  5. Schaefer, H. H., Banach Lattices and Positive Operators, Die Grundlehren der mathematischen Wissenschaften 215, Springer-Verlag, Berlin and New York (1974). (1974) Zbl0296.47023MR0423039
  6. Meyer-Nieberg, P., Banach lattices, Universitext. Springer-Verlag, Berlin (1991). (1991) Zbl0743.46015MR1128093
  7. Wickstead, A. W., 10.1017/S0305004100074752, Math. Proc. Camb. Philos. Soc. 120 (1996), 175-179. (1996) Zbl0872.47018MR1373356DOI10.1017/S0305004100074752
  8. Wnuk, W., Some characterizations of Banach lattices with the Schur property, Congress on Functional Analysis (Madrid, 1988). Rev. Mat. Univ. Complutense Madr. , No. Suppl., (1989), 217-224. (1989) Zbl0717.46018MR1057221
  9. Zaanen, A. C., Riesz Spaces II, North-Holland Mathematical Library 30, Amsterdam-New York-Oxford, North-Holland Publishing Company (1983). (1983) Zbl0519.46001MR0704021

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