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Keywords:
AM-compact operator; order weakly compact operator; b-weakly compact operator; almost Dunford-Pettis operator; b-AM-compact operator; order continuous norm; discrete Banach lattice
AM-compact operator; order weakly compact operator; b-weakly compact operator; almost Dunford-Pettis operator; b-AM-compact operator; order continuous norm; discrete Banach lattice
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.
References:
[1] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces. Academic Press, New York-London, 1978. MR 0493242 | Zbl 1043.46003
[2] Aliprantis C.D., Burkinshaw O.: Positive Operators. reprint of the 1985 original, Springer, Dordrecht, 2006. MR 2262133 | Zbl 1098.47001
[3] Alpay S., Altin B., Tonyali C.: On property $(b)$ of vector lattices. Positivity 7 (2003), no. 1–2, 135–139. DOI 10.1023/A:1025840528211 | MR 2028377 | Zbl 1036.46018
[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
[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. DOI 10.1090/S0002-9939-06-08585-6 | MR 2262919 | Zbl 1118.47029
[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. DOI 10.1007/BF03032084 | MR 2376267 | Zbl 1140.47029
[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. DOI 10.1007/s11117-008-2288-6 | MR 2538515 | Zbl 1191.47024
[8] Aqzzouz B., Hmichane J.: The class of b-AM-compact operators. Quaestiones Mathematicae(to appear).
[9] Aqzzouz B., Elbour A.: Some characterizations of almost Dunford-Pettis operators and applications. Positivity 15 (2011), 369–380. DOI 10.1007/s11117-010-0083-7 | MR 2832593 | Zbl 1244.47034
[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.
[11] Chen Z.L., Wickstead A.W.: Some applications of Rademacher sequences in Banach lattices. Positivity 2 (1998), no. 2, 171–191. DOI 10.1023/A:1009767118180 | MR 1656870 | Zbl 0967.46019
[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. DOI 10.1016/S0019-3577(98)80017-7 | MR 1691436 | Zbl 0922.46017
[13] Dodds P.G.: o-Weakly compact mappings of vector lattices. Trans. Amer. Math. Soc. 214 (1975), 389–402. DOI 10.2307/1997114 | MR 0385629
[14] Dodds P.G., Fremlin D.H.: Compact operators on Banach lattices. Israel J. Math. 34 (1979) 287-320. DOI 10.1007/BF02760610 | MR 0570888
[15] Grothendieck A.: Sur les applications linéaires faiblement compactes d'espaces du type $C(K)$. Canad. J. Math. 5 (1953), 129–173. DOI 10.4153/CJM-1953-017-4 | MR 0058866 | Zbl 0050.10902
[16] Holub J.R.: A note on Dunford-Pettis operators. Glasgow Math. J. 29 (1987), no. 2, 271–273. DOI 10.1017/S0017089500006935 | MR 0901675 | Zbl 0746.47015
[17] Meyer-Nieberg P.: Banach lattices. Universitext, Springer, Berlin, 1991. MR 1128093 | Zbl 0743.46015
[18] Sanchez J.A.: Operators on Banach lattices (Spanish). Ph.D. Thesis, Complutense University, Madrid, 1985.
[19] Wickstead A.W.: Converses for the Dodds-Fremlin and Kalton-Saab Theorems. Math. Proc. Camb. Philos. Soc. 120 (1996), 175–179. DOI 10.1017/S0305004100074752 | MR 1373356 | Zbl 0872.47018
[20] Wnuk W.: Banach lattices with the weak Dunford-Pettis property. Atti Sem. Mat. Fis. Univ. Modena 42 (1994), no. 1, 227–236. MR 1282338 | Zbl 0805.46023
[21] Zaanen A.C.: Riesz Spaces II. North Holland Publishing Co., Amsterdam, 1983. MR 0704021 | Zbl 0519.46001
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