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Bourgain, J.

On the Dunford-Pettis property. (English) Zbl 0463.46027

Proc. Am. Math. Soc. 81, 265-272 (1981).
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Cited in 14 Documents

MSC:

46E40 Spaces of vector- and operator-valued functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A50 Compactness in topological linear spaces; angelic spaces, etc.
03C20 Ultraproducts and related constructions

Keywords:

Dunford-Pettis property; weakly conditionally compact; Bochner space; ultrapowers; projection constants; unconditional bases
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\textit{J. Bourgain}, Proc. Am. Math. Soc. 81, 265--272 (1981; Zbl 0463.46027)
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References:

[1] J. Bourgain, An averaging result for \?\textonesuperior -sequences and applications to weakly conditionally compact sets in \?\textonesuperior _{\?}, Israel J. Math. 32 (1979), no. 4, 289 – 298. · Zbl 0464.60005
[2] 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
[3] T. Figiel, J. Lindenstrauss, and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), no. 1-2, 53 – 94. · Zbl 0375.52002
[4] Stefan Heinrich, Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72 – 104. · Zbl 0412.46017
[5] J. L. Krivine, Langages à valeurs réelles et applications (to appear). · Zbl 0292.02019
[6] J. Lindenstrauss and H. P. Rosenthal, The \cal\?_{\?} spaces, Israel J. Math. 7 (1969), 325 – 349. · Zbl 0205.12602
[7] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. · Zbl 0259.46011
[8] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Springer-Verlag, Berlin-New York, 1977. Sequence spaces; Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. · Zbl 0362.46013
[9] Haskell P. Rosenthal, A characterization of Banach spaces containing \?\textonesuperior , Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411 – 2413. · Zbl 0297.46013
[10] -, The Banach spaces \( C(K)\) and \( {L^p}(\mu )\), Bull. Amer. Math. Soc. 81 (1975), 763-781. · Zbl 0334.46033
[11] Gilles Pisier, Une propriété de stabilité de la classe des espaces ne contenant pas \?\textonesuperior , C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 17, A747 – A749 (French, with English summary). · Zbl 0373.46033
[12] H. Schaefer, Banach lattices and positive linear operators, Springer-Verlag, Berlin and New York. · Zbl 0296.47023
[13] Jacques Stern, Some applications of model theory in Banach space theory, Ann. Math. Logic 9 (1976), no. 1-2, 49 – 121. · Zbl 0378.02026
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