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Dunford-Pettis operators on Banach lattices. (English) Zbl 0498.47013

MSC:
47B60 Linear operators on ordered spaces
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
46B42 Banach lattices
46A40 Ordered topological linear spaces, vector lattices
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[1] Charalambos D. Aliprantis and Owen Burkinshaw, Locally solid Riesz spaces, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics, Vol. 76. · Zbl 0402.46005
[2] Charalambos D. Aliprantis and Owen Burkinshaw, Positive compact operators on Banach lattices, Math. Z. 174 (1980), no. 3, 289 – 298. · Zbl 0425.46015 · doi:10.1007/BF01161416 · doi.org
[3] C. D. Aliprantis and O. Burkinshaw, On weakly compact operators on Banach lattices, Proc. Amer. Math. Soc. 83 (1981), no. 3, 573 – 578. · Zbl 0452.47038
[4] Kevin T. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), no. 1, 35 – 41. · Zbl 0398.46025 · doi:10.1007/BF01406706 · doi.org
[5] J. Bourgain, Dunford-Pettis operators on \?\textonesuperior and the Radon-NikodĂ˝m property, Israel J. Math. 37 (1980), no. 1-2, 34 – 47. , https://doi.org/10.1007/BF02762866 J. Bourgain, A characterization of non-Dunford-Pettis operators on \?\textonesuperior , Israel J. Math. 37 (1980), no. 1-2, 48 – 53. · Zbl 0457.46018 · doi:10.1007/BF02762867 · doi.org
[6] O. Burkinshaw, Weak compactness in the order dual of a vector lattice, Ph. D. thesis, Purdue University, 1972. · Zbl 0282.46007
[7] J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. · Zbl 0369.46039
[8] P. G. Dodds, \?-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214 (1975), 389 – 402. · Zbl 0313.46011
[9] P. G. Dodds and D. H. Fremlin, Compact operators in Banach lattices, Israel J. Math. 34 (1979), no. 4, 287 – 320 (1980). · Zbl 0438.47042 · doi:10.1007/BF02760610 · doi.org
[10] Michel Duhoux, \?-weakly compact mappings from a Riesz space to a locally convex space, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 22(70) (1978), no. 4, 371 – 378. · Zbl 0409.46007
[11] Helmut H. Schaefer, Banach lattices and positive operators, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 215. · Zbl 0296.47023
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