Banach spaces which are $M$-ideals in their bidual have property $\left(u\right)$
Annales de l'Institut Fourier, Tome 39 (1989) no. 2, pp. 361-371.

Nous montrons que tout espace de Banach qui est $M$-idéal de son bidual a la propriété $\left(u\right)$ de A. Pelczynski, et mentionnons quelques conséquences.

We show that every Banach space which is an $M$-ideal in its bidual has the property $\left(u\right)$ of Pelczynski. Several consequences are mentioned.

@article{AIF_1989__39_2_361_0,
author = {Godefroy, Gilles and Li, D.},
title = {Banach spaces which are $M$-ideals in their bidual have property $(u)$},
journal = {Annales de l'Institut Fourier},
pages = {361--371},
publisher = {Institut Fourier},
volume = {39},
number = {2},
year = {1989},
doi = {10.5802/aif.1170},
zbl = {0659.46014},
mrnumber = {90j:46020},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1170/}
}
Godefroy, Gilles; Li, D. Banach spaces which are $M$-ideals in their bidual have property $(u)$. Annales de l'Institut Fourier, Tome 39 (1989) no. 2, pp. 361-371. doi : 10.5802/aif.1170. http://www.numdam.org/articles/10.5802/aif.1170/

[1] E. M. Alfsen, E. G. Effros, Structure in real Banach spaces I, Ann. of Math., 96 (1972), 98-128. | MR 50 #5432 | Zbl 0248.46019

[2] E. Behrends, M-structure and the Banach-Stone theorem, Lecture Notes in Mathematics 736, Springer-Verlag (1977). | MR 81b:46002 | Zbl 0436.46013

[3] E. Behrends, P. Harmand, Banach spaces which are proper M-ideals, Studia Mathematica, 81 (1985), 159-169. | MR 87f:46031 | Zbl 0529.46015

[4] G. A. Edgar, An ordering of Banach spaces, Pacific J. of Maths, 108, 1 (1983), 83-98. | MR 84k:46012 | Zbl 0533.46007

[5] G. Godefroy, On Riesz subsets of abelian discrete groups, Israel J. of Maths, 61, 3 (1988), 301-331. | MR 89m:43011 | Zbl 0661.43003

[6] G. Godefroy, P. Saab, Weakly unconditionally convergent series in M-ideals, Math. Scand., to appear. | Zbl 0676.46006

[7] G. Godefroy, M. Talagrand, Nouvelles classes d'espaces de Banach à predual unique, Séminaire d'Ana. Fonct. de l'École Polytechnique, Exposé n° 6 (1980/1981). | Numdam | Zbl 0475.46013

[8] G. Godefroy, Existence and uniqueness of isometric preduals : a survey, in Banach space Theory, Proceedings of a Research workshop held July 5-25, 1987, Contemporary Mathematics vol. 85 (1989), 131-194. | Zbl 0674.46010

[9] G. Godefroy, D. Li, Some natural families of M-ideals, to appear. | Zbl 0687.46010

[10] P. Harmand, A. Lima, On spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc., 283-1 (1984), 253-264. | MR 86b:46016 | Zbl 0545.46009

[11] A. Lima, M-ideals of compact operators in classical Banach spaces, Math. Scand., 44 (1979), 207-217. | EuDML 166642 | MR 81c:47047 | Zbl 0407.46019

[12] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces, Vol. II, Springer-Verlag (1979). | MR 81c:46001 | Zbl 0403.46022

[13] F. Lust, Produits tensoriels projectifs d'espaces de Banach faiblement sequentiellement complets, Coll. Math., 36-2 (1976), 255-267. | EuDML 263584 | MR 55 #11072 | Zbl 0356.46058

[14] A. Pelczynski, Banach spaces on which every unconditionally convergent operator is weakly compact, Bull. Acad. Pol. Sciences, 10 (1962), 641-648. | MR 26 #6785 | Zbl 0107.32504

[15] R. R. Smith, J. D. Ward, Applications of convexity and M-ideal theory to quotient Banach algebras, Quart. J. of Maths. Oxford, 2-30 (1978), 365-384. | Zbl 0412.46042