| Title:
|
On the equality between some classes of operators on Banach lattices (English) |
| Author:
|
Aqzzouz, Belmesnaoui |
| Author:
|
Elbour, Aziz |
| Author:
|
Moussa, Mohammed |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
347-354 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
M-weakly compact operator |
| Keyword:
|
L-weakly compact operator |
| Keyword:
|
Dunford-Pettis operator |
| Keyword:
|
weakly compact operator |
| Keyword:
|
semi-compact operator |
| Keyword:
|
compact operator |
| Keyword:
|
order continuous norm |
| Keyword:
|
discrete Banach lattice |
| Keyword:
|
positive Schur property |
| MSC:
|
46A40 |
| MSC:
|
46B28 |
| MSC:
|
46B40 |
| MSC:
|
46B42 |
| MSC:
|
47B65 |
| idZBL:
|
Zbl 1265.46035 |
| idMR:
|
MR3112492 |
| DOI:
|
10.21136/MB.2012.142899 |
| . |
| Date available:
|
2012-08-19T21:32:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142899 |
| . |
| Reference:
|
[1] D., Aliprantis C., O., Burkinshaw: Locally Solid Riesz Spaces.Academic Press, Providence, RI (1978). Zbl 0402.46005, MR 0493242 |
| Reference:
|
[2] D., Aliprantis C., O., Burkinshaw: Dunford-Pettis operators on Banach lattices.Trans. Amer. Math. Soc. 274 (1982), 227-238. Zbl 0498.47013, MR 0670929, 10.1090/S0002-9947-1982-0670929-1 |
| Reference:
|
[3] D., Aliprantis C., O., Burkinshaw: Positive Operators.Pure and Applied Mathematics, 119. Academic Press, Inc., Orlando, FL (1985). Zbl 0608.47039, MR 0809372 |
| Reference:
|
[4] D., Aliprantis C., O., Burkinshaw: On the ring ideal generated by a positive operator.J. Funct. Anal. 67 (1986), 60-72. Zbl 0588.47044, MR 0842603, 10.1016/0022-1236(86)90043-1 |
| Reference:
|
[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. Zbl 1099.46016, MR 2196052, 10.1090/S0002-9939-05-08083-4 |
| Reference:
|
[6] B., Aqzzouz, R., Nouira, L., Zraoula: About positive Dunford-Pettis operators on Banach lattices.J. Math. Anal. Appl. 324 (2006), 49-59. Zbl 1112.47028, MR 2262455, 10.1016/j.jmaa.2005.10.083 |
| Reference:
|
[7] B., Aqzzouz, R., Nouira, L., Zraoula: Semi-compactness of positive Dunford-Pettis operators.Proc. Amer. Math. Soc. 136 (2008), 1997-2006. Zbl 1152.47012, MR 2383506, 10.1090/S0002-9939-08-09032-1 |
| Reference:
|
[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. Zbl 1166.47036, MR 2452672, 10.1007/s12215-008-0021-8 |
| Reference:
|
[9] L., Chen Z., W., Wickstead A.: L-weakly and M-weakly compact operators.Indag. Math. (N.S.) 10 (1999), 321-336. Zbl 1028.47028, MR 1819891, 10.1016/S0019-3577(99)80025-1 |
| Reference:
|
[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). Zbl 1202.47041, MR 2639440, 10.1007/s12215-010-0006-2 |
| Reference:
|
[11] G., Dodds P., H., Fremlin D.: Compact operators on Banach lattices.Israel J. Math. 34 (1979), 287-320. MR 0570888, 10.1007/BF02760610 |
| Reference:
|
[12] J., Kalton N., P., Saab: Ideal properties of regular operators between Banach lattices.Ill. J. Math. 29 (1985), 382-400. MR 0786728, 10.1215/ijm/1256045630 |
| Reference:
|
[13] Meyer-Nieberg, P.: Banach Lattices. Universitext.Springer, Berlin (1991). MR 1128093 |
| Reference:
|
[14] W., Wickstead A.: Converses for the Dodds-Fremlin and Kalton-Saab Theorems.Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. Zbl 0872.47018, MR 1373356, 10.1017/S0305004100074752 |
| Reference:
|
[15] W., Wnuk: A note on the positive Schur property.Glasgow Math. J. 31 (1989), 169-172. Zbl 0694.46020, MR 0997812, 10.1017/S0017089500007692 |
| Reference:
|
[16] C., Zaanen A.: Riesz Spaces II.North Holland, Amsterdam (1983). Zbl 0519.46001, MR 0704021 |
| . |
