| Title:
|
AM-Compactness of some classes of operators (English) |
| Author:
|
Aqzzouz, Belmesnaoui |
| Author:
|
H'michane, Jawad |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
509-518 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact. (English) |
| Keyword:
|
AM-compact operator |
| Keyword:
|
order weakly compact operator |
| Keyword:
|
b-weakly compact operator |
| Keyword:
|
almost Dunford-Pettis operator |
| Keyword:
|
b-AM-compact operator |
| Keyword:
|
order continuous norm |
| Keyword:
|
discrete Banach lattice |
| MSC:
|
46A40 |
| MSC:
|
46B40 |
| MSC:
|
46B42 |
| idMR:
|
MR3016422 |
| . |
| Date available:
|
2013-03-02T13:35:32Z |
| Last updated:
|
2015-02-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143185 |
| . |
| Reference:
|
[1] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces.Academic Press, New York-London, 1978. Zbl 1043.46003, MR 0493242 |
| Reference:
|
[2] Aliprantis C.D., Burkinshaw O.: Positive Operators.reprint of the 1985 original, Springer, Dordrecht, 2006. Zbl 1098.47001, MR 2262133 |
| Reference:
|
[3] Alpay S., Altin B., Tonyali C.: On property $(b)$ of vector lattices.Positivity 7 (2003), no. 1–2, 135–139. Zbl 1036.46018, MR 2028377, 10.1023/A:1025840528211 |
| Reference:
|
[4] Alpay S., Altin B.: On Riesz spaces with $b$-property and $b$-weakly compact operators.Vladikavkaz. Mat. Zh. 11 (2009), no. 2, 19–26. MR 2529405 |
| Reference:
|
[5] Aqzzouz B., Nouira R., Zraoula L.: Compactness properties of operators dominated by AM-compact operators.Proc. Amer. Math. Soc. 135 (2007), no. 4, 1151–1157. Zbl 1118.47029, MR 2262919, 10.1090/S0002-9939-06-08585-6 |
| Reference:
|
[6] Aqzzouz B., Zraoula L.: AM-compactness of positive Dunford-Pettis operators on Banach lattices.Rend. Circ. Mat. Palermo (2) 56 (2007), no. 3, 305–316. Zbl 1140.47029, MR 2376267, 10.1007/BF03032084 |
| Reference:
|
[7] Aqzzouz B., Elbour A., Hmichane J.: The duality problem for the class of $b$-weakly compact operators.Positivity 13 (2009) no. 4, 683–692. Zbl 1191.47024, MR 2538515, 10.1007/s11117-008-2288-6 |
| Reference:
|
[8] Aqzzouz B., Hmichane J.: The class of b-AM-compact operators.Quaestiones Mathematicae(to appear). |
| Reference:
|
[9] Aqzzouz B., Elbour A.: Some characterizations of almost Dunford-Pettis operators and applications.Positivity 15 (2011), 369–380. Zbl 1244.47034, MR 2832593, 10.1007/s11117-010-0083-7 |
| Reference:
|
[10] Aqzzouz B., Hmichane J.: The b-weak compactness of order weakly compact operators.Complex Anal. Oper. Theory, DOI 10. 1007/s 11785-011-0138-1. |
| Reference:
|
[11] Chen Z.L., Wickstead A.W.: Some applications of Rademacher sequences in Banach lattices.Positivity 2 (1998), no. 2, 171–191. Zbl 0967.46019, MR 1656870, 10.1023/A:1009767118180 |
| Reference:
|
[12] Chen Z.L., Wickstead A.W.: Relative weak compactness of solid hulls in Banach lattices.Indag. Math. (N.S.) 9 (1998), no. 2, 187–196. Zbl 0922.46017, MR 1691436, 10.1016/S0019-3577(98)80017-7 |
| Reference:
|
[13] Dodds P.G.: o-Weakly compact mappings of vector lattices.Trans. Amer. Math. Soc. 214 (1975), 389–402. MR 0385629, 10.2307/1997114 |
| Reference:
|
[14] Dodds P.G., Fremlin D.H.: Compact operators on Banach lattices.Israel J. Math. 34 (1979) 287-320. MR 0570888, 10.1007/BF02760610 |
| Reference:
|
[15] Grothendieck A.: Sur les applications linéaires faiblement compactes d'espaces du type $C(K)$.Canad. J. Math. 5 (1953), 129–173. Zbl 0050.10902, MR 0058866, 10.4153/CJM-1953-017-4 |
| Reference:
|
[16] Holub J.R.: A note on Dunford-Pettis operators.Glasgow Math. J. 29 (1987), no. 2, 271–273. Zbl 0746.47015, MR 0901675, 10.1017/S0017089500006935 |
| Reference:
|
[17] Meyer-Nieberg P.: Banach lattices.Universitext, Springer, Berlin, 1991. Zbl 0743.46015, MR 1128093 |
| Reference:
|
[18] Sanchez J.A.: Operators on Banach lattices (Spanish)., Ph.D. Thesis, Complutense University, Madrid, 1985. |
| Reference:
|
[19] Wickstead A.W.: Converses for the Dodds-Fremlin and Kalton-Saab Theorems.Math. Proc. Camb. Philos. Soc. 120 (1996), 175–179. Zbl 0872.47018, MR 1373356, 10.1017/S0305004100074752 |
| Reference:
|
[20] Wnuk W.: Banach lattices with the weak Dunford-Pettis property.Atti Sem. Mat. Fis. Univ. Modena 42 (1994), no. 1, 227–236. Zbl 0805.46023, MR 1282338 |
| Reference:
|
[21] Zaanen A.C.: Riesz Spaces II.North Holland Publishing Co., Amsterdam, 1983. Zbl 0519.46001, MR 0704021 |
| . |
