Geodesic
On the equality between some classes of operators on Banach lattices
Mathematica Bohemica, Tome 137 (2012) no. 3, pp. 347-354
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
DOI : 10.21136/MB.2012.142899
Classification : 46A40, 46B28, 46B40, 46B42, 47B65
Keywords: M-weakly compact operator; L-weakly compact operator; Dunford-Pettis operator; weakly compact operator; semi-compact operator; compact operator; order continuous norm; discrete Banach lattice; positive Schur property 
@article{10_21136_MB_2012_142899,
     author = {Aqzzouz, Belmesnaoui and Elbour, Aziz and Moussa, Mohammed},
     title = {On the equality between some classes of operators on {Banach} lattices},
     journal = {Mathematica Bohemica},
     pages = {347--354},
     year = {2012},
     volume = {137},
     number = {3},
     doi = {10.21136/MB.2012.142899},
     mrnumber = {3112492},
     zbl = {1265.46035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142899/}
}
TY  - JOUR
AU  - Aqzzouz, Belmesnaoui
AU  - Elbour, Aziz
AU  - Moussa, Mohammed
TI  - On the equality between some classes of operators on Banach lattices
JO  - Mathematica Bohemica
PY  - 2012
SP  - 347
EP  - 354
VL  - 137
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142899/
DO  - 10.21136/MB.2012.142899
LA  - en
ID  - 10_21136_MB_2012_142899
ER  - 
%0 Journal Article
%A Aqzzouz, Belmesnaoui
%A Elbour, Aziz
%A Moussa, Mohammed
%T On the equality between some classes of operators on Banach lattices
%J Mathematica Bohemica
%D 2012
%P 347-354
%V 137
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142899/
%R 10.21136/MB.2012.142899
%G en
%F 10_21136_MB_2012_142899
Aqzzouz, Belmesnaoui; Elbour, Aziz; Moussa, Mohammed. On the equality between some classes of operators on Banach lattices. Mathematica Bohemica, Tome 137 (2012) no. 3, pp. 347-354. doi: 10.21136/MB.2012.142899

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

[2] D., Aliprantis C., O., Burkinshaw: Dunford-Pettis operators on Banach lattices. Trans. Amer. Math. Soc. 274 (1982), 227-238. | DOI | MR | Zbl

[3] D., Aliprantis C., O., Burkinshaw: Positive Operators. Pure and Applied Mathematics, 119. Academic Press, Inc., Orlando, FL (1985). | MR | Zbl

[4] D., Aliprantis C., O., Burkinshaw: On the ring ideal generated by a positive operator. J. Funct. Anal. 67 (1986), 60-72. | DOI | MR | Zbl

[5] B., Aqzzouz, R., Nouira, L., Zraoula: Les opérateurs de Dunford-Pettis positifs qui sont faiblement compacts. Proc. Amer. Math. Soc. 134 (2006), 1161-1165. | DOI | MR | Zbl

[6] B., Aqzzouz, R., Nouira, L., Zraoula: About positive Dunford-Pettis operators on Banach lattices. J. Math. Anal. Appl. 324 (2006), 49-59. | DOI | MR | Zbl

[7] B., Aqzzouz, R., Nouira, L., Zraoula: Semi-compactness of positive Dunford-Pettis operators. Proc. Amer. Math. Soc. 136 (2008), 1997-2006. | DOI | MR | Zbl

[8] B., Aqzzouz, R., Nouira, L., Zraoula: On the duality problem of positive Dunford-Pettis operators on Banach lattices. Rend. Circ. Mat. Palermo 57 (2008), 287-294. | DOI | MR | Zbl

[9] L., Chen Z., W., Wickstead A.: L-weakly and M-weakly compact operators. Indag. Math. (N.S.) 10 (1999), 321-336. | DOI | MR | Zbl

[10] N., Cheng, L., Chen Z., Y., Feng: L and M-weak compactness of positive semi-compact operators. Rend. Circ. Mat. Palermo 59 101-105 (2010). | DOI | MR | Zbl

[11] G., Dodds P., H., Fremlin D.: Compact operators on Banach lattices. Israel J. Math. 34 (1979), 287-320. | DOI | MR

[12] J., Kalton N., P., Saab: Ideal properties of regular operators between Banach lattices. Ill. J. Math. 29 (1985), 382-400. | DOI | MR

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

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

[15] W., Wnuk: A note on the positive Schur property. Glasgow Math. J. 31 (1989), 169-172. | DOI | MR | Zbl

[16] C., Zaanen A.: Riesz Spaces II. North Holland, Amsterdam (1983). | MR | Zbl

Cité par Sources :