Geodesic
Some characterizations of order weakly compact operator
Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 105-112
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/MB.2011.141454
Classification : 46A40, 46B40, 46B42, 47B07, 47B60
Keywords: order weakly compact operator; order continuous norm; discrete Banach lattice; weakly sequentially continuous lattice operations 
@article{10_21136_MB_2011_141454,
     author = {Aqzzouz, Belmesnaoui and Elbour, Aziz},
     title = {Some characterizations of order weakly compact operator},
     journal = {Mathematica Bohemica},
     pages = {105--112},
     year = {2011},
     volume = {136},
     number = {1},
     doi = {10.21136/MB.2011.141454},
     mrnumber = {2807713},
     zbl = {1224.46035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141454/}
}
TY  - JOUR
AU  - Aqzzouz, Belmesnaoui
AU  - Elbour, Aziz
TI  - Some characterizations of order weakly compact operator
JO  - Mathematica Bohemica
PY  - 2011
SP  - 105
EP  - 112
VL  - 136
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141454/
DO  - 10.21136/MB.2011.141454
LA  - en
ID  - 10_21136_MB_2011_141454
ER  - 
%0 Journal Article
%A Aqzzouz, Belmesnaoui
%A Elbour, Aziz
%T Some characterizations of order weakly compact operator
%J Mathematica Bohemica
%D 2011
%P 105-112
%V 136
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141454/
%R 10.21136/MB.2011.141454
%G en
%F 10_21136_MB_2011_141454
Aqzzouz, Belmesnaoui; Elbour, Aziz. Some characterizations of order weakly compact operator. Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 105-112. doi: 10.21136/MB.2011.141454

[1] Aliprantis, C. D., Burkinshaw, O.: Locally Solid Riesz Spaces. Academic Press (1978). | MR | Zbl

[2] Aliprantis, C. D., Burkinshaw, O.: Positive Operators. Reprint of the 1985 original. Springer, Dordrecht (2006). | MR | Zbl

[3] Dodds, P. G.: o-weakly compact mappings of Riesz spaces. Trans. Amer. Math. Soc. 214 (1975), 389-402. | MR | Zbl

[4] Meyer-Nieberg, P.: Banach Lattices. Universitext. Springer, Berlin (1991). | MR | Zbl

[5] Wickstead, A. W.: Converses for the Dodds-Fremlin and Kalton-Saab Theorems. Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. | DOI | MR | Zbl

Cité par Sources :