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Dunford-Pettis sets in the space of Bochner integrable functions. (English) Zbl 0398.46025

MSC:
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E40 Spaces of vector- and operator-valued functions
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References:
[1] Bourgain, J.: An averaging result forl 1-sequences and application to weakly conditionally compact sets inL 1(?,X) (preprint)
[2] Brooks, J.K., Dinculeanu, N.: Weak compactness in the space of Bochner integrable functions and applications. Advances in Math.24, 172-188 (1977) · Zbl 0354.46026 · doi:10.1016/S0001-8708(77)80017-0
[3] Davis, W.J., Figiel, T., Johnson, W.B., Pelczynski, A.: Factoring weakly compact operators. J. Funct. Anal.17, 311-327 (1974) · Zbl 0306.46020 · doi:10.1016/0022-1236(74)90044-5
[4] Diestel, J.: Remarks on weak compactness inL 1(?,X). Glasgow Math. J.18, 87-91 (1977) · Zbl 0342.46020 · doi:10.1017/S0017089500003074
[5] Diestel, J., Uhl, J.J., Jr.: Vector measures. Math. Surveys No. 15, American Mathematics Society, Providence 1977 · Zbl 0369.46039
[6] Dinculeanu, N.: Vector measures. New York: Pergamon Press 1967 · Zbl 0156.14902
[7] Rosenthal, H.P.: A characterization of Banach spaces containingl 1. Proc. Nat. Acad. Sci. USA71, 2411-2413 (1974) · Zbl 0297.46013 · doi:10.1073/pnas.71.6.2411
[8] Rosenthal, H.P.: Pointwise compact subsets of the first Baire class. Amer. J. Math.99, 362-378 (1977) · Zbl 0392.54009 · doi:10.2307/2373824
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