Some characterizations of order weakly compact operator

Belmesnaoui Aqzzouz; Aziz Elbour

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 1, page 105-112
  • ISSN: 0862-7959

Abstract

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We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.

How to cite

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Aqzzouz, Belmesnaoui, and Elbour, Aziz. "Some characterizations of order weakly compact operator." Mathematica Bohemica 136.1 (2011): 105-112. <http://eudml.org/doc/196862>.

@article{Aqzzouz2011,
abstract = {We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.},
author = {Aqzzouz, Belmesnaoui, Elbour, Aziz},
journal = {Mathematica Bohemica},
keywords = {order weakly compact operator; order continuous norm; discrete Banach lattice; weakly sequentially continuous lattice operations; order weakly compact operator; order continuous norm; discrete Banach lattice; weakly sequentially continuous lattice operation},
language = {eng},
number = {1},
pages = {105-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some characterizations of order weakly compact operator},
url = {http://eudml.org/doc/196862},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Aqzzouz, Belmesnaoui
AU - Elbour, Aziz
TI - Some characterizations of order weakly compact operator
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 1
SP - 105
EP - 112
AB - We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.
LA - eng
KW - order weakly compact operator; order continuous norm; discrete Banach lattice; weakly sequentially continuous lattice operations; order weakly compact operator; order continuous norm; discrete Banach lattice; weakly sequentially continuous lattice operation
UR - http://eudml.org/doc/196862
ER -

References

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  1. Aliprantis, C. D., Burkinshaw, O., Locally Solid Riesz Spaces, Academic Press (1978). (1978) Zbl0402.46005MR0493242
  2. Aliprantis, C. D., Burkinshaw, O., Positive Operators, Reprint of the 1985 original. Springer, Dordrecht (2006). (2006) Zbl1098.47001MR2262133
  3. Dodds, P. G., o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214 (1975), 389-402. (1975) Zbl0313.46011MR0385629
  4. Meyer-Nieberg, P., Banach Lattices, Universitext. Springer, Berlin (1991). (1991) Zbl0743.46015MR1128093
  5. Wickstead, A. W., 10.1017/S0305004100074752, Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. (1996) Zbl0872.47018MR1373356DOI10.1017/S0305004100074752

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