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Keywords:
b-weakly compact operator; b-AM-compact operator; strong type (B) operator; order continuous norm; positive Schur property
b-weakly compact operator; b-AM-compact operator; strong type (B) operator; order continuous norm; positive Schur property
Summary:
We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).
References:
[1] Aliprantis C.D., Burkinshaw O.: Positive Operators. reprint of the 1985 original, Springer, Dordrecht, 2006. MR 2262133 | Zbl 1098.47001
[2] Altin B.: Some properties of b-weakly compact operators. Gazi University Journal of Science 18 (3) (2005), 391–395.
[3] Altin B.: On b-weakly compact operators on Banach lattices. Taiwanese J. Math. 11 (2007), 143–150. MR 2304011 | Zbl 1139.47018
[4] 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
[5] Alpay S., Altin B., Tonyali C.: A note on Riesz spaces with property-b. Czechoslovak Math. J. 56 (131) (2006), no. 2, 765–772. DOI 10.1007/s10587-006-0054-0 | MR 2291773 | Zbl 1164.46310
[6] Alpay S., Altin B.: A note on b-weakly compact operators. Positivity 11 (2007), no. 4, 575–582. DOI 10.1007/s11117-007-2110-x | MR 2346443 | Zbl 1137.47028
[7] Alpay S., Ercan Z.: Characterizations of Riesz spaces with b-property. Positivity 13 (2009), no. 1, 21–30. DOI 10.1007/s11117-008-2227-6 | MR 2466226 | Zbl 1167.46001
[8] Alpay S., Altin B.: On operators of strong type B. preprint.
[9] Aqzzouz B., Elbour A., Hmichane J.: Some properties of the class of positive Dunford-Pettis operators. J. Math. Anal. Appl. 354 (2009), 295–300. DOI 10.1016/j.jmaa.2008.12.063 | MR 2510440 | Zbl 1167.47033
[10] Aqzzouz B., Hmichane J.: The class of b-AM-compact operators. Quaestions Mathematicae(to appear).
[11] Aqzzouz B., Elbour A.: On the weak compactness of b-weakly compact operators. Positivity 14 (2010), no. 1, 75–81. DOI 10.1007/s11117-009-0006-7 | MR 2596465 | Zbl 1198.47034
[12] Aqzzouz B., Elbour A., Hmichane J.: On some properties of the class of semi-compact operators. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 4, 761–767. MR 2918181 | Zbl 1250.47020
[13] Aqzzouz B., Hmichane J.: The b-weak compactness of order weakly compact operators. Complex Anal. Oper. Theory 7 (2013), no. 1, 3–8, DOI 10.1007/s 11785-011-0138-1. DOI 10.1007/s11785-011-0138-1 | MR 3010785
[14] Aqzzouz B., Elbour A.: The b-weakly compactness of semi-compact operators. Acta Sci. Math. (Szeged) 76 (2010), 501–510. MR 2789684 | Zbl 1235.47018
[15] Aqzzouz B., Elbour A., Moussa M., Hmichane J.: Some characterizations of b-weakly compact operators. Math. Rep. (Bucur.) 12 (62) (2010), no. 4, 315–324. MR 2777361 | Zbl 1235.47019
[16] Aqzzouz B., Hmichane J., Aboutafail O.: Compactness of b-weakly compact operators. Acta Sci. Math. (Szeged) 78 (2012), 163–171. Zbl 1261.47059
[17] Chen Z.L., Wickstead A.W.: L-weakly and M-weakly compact operators. Indag. Math. (N.S.) 10 (1999), no. 3, 321–336. DOI 10.1016/S0019-3577(99)80025-1 | MR 1819891 | Zbl 1028.47028
[18] Cheng Na, Chen Zi-li: b-AM-compact operators on Banach lattices. Chin. J. Eng. Math. 27 (2010), no. 4, ID: 1005–3085. MR 2777452 | Zbl 1235.47020
[19] Ghoussoub N., Johnson W.B.: Counterexamples to several problems on the factorization of bounded linear operators. Proc. Amer. Math. Soc. 92 (1984), no. 2, 233–238. DOI 10.1090/S0002-9939-1984-0754710-8 | MR 0754710 | Zbl 0615.46022
[20] Niculescu C.: Order $\sigma$-continuous Operators on Banach Lattices. Lecture Notes in Mathematics, 991, Springer, Berlin, 1983. DOI 10.1007/BFb0061571 | MR 0714186 | Zbl 0515.47016
[21] Zaanen A.C.: Introduction to Operator Theory in Riesz Spaces. Springer, Berlin, 1997. MR 1631533 | Zbl 0878.47022
[22] Meyer-Nieberg P.: Banach Lattices. Universitext, Springer, Berlin, 1991. MR 1128093 | Zbl 0743.46015
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