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

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

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

@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},
     address = {Grenoble},
     volume = {39},
     number = {2},
     year = {1989},
     doi = {10.5802/aif.1170},
     mrnumber = {90j:46020},
     zbl = {0659.46014},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1170/}
}
TY  - JOUR
AU  - Godefroy, Gilles
AU  - Li, D.
TI  - Banach spaces which are $M$-ideals in their bidual have property $(u)$
JO  - Annales de l'Institut Fourier
PY  - 1989
SP  - 361
EP  - 371
VL  - 39
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.1170/
DO  - 10.5802/aif.1170
LA  - en
ID  - AIF_1989__39_2_361_0
ER  - 
%0 Journal Article
%A Godefroy, Gilles
%A Li, D.
%T Banach spaces which are $M$-ideals in their bidual have property $(u)$
%J Annales de l'Institut Fourier
%D 1989
%P 361-371
%V 39
%N 2
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.1170/
%R 10.5802/aif.1170
%G en
%F AIF_1989__39_2_361_0
Godefroy, Gilles; Li, D. Banach spaces which are $M$-ideals in their bidual have property $(u)$. Annales de l'Institut Fourier, Volume 39 (1989) no. 2, pp. 361-371. doi : 10.5802/aif.1170. http://archive.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 | Zbl

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

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

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

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

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

[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

[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

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

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

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

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

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

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

[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

Cited by Sources: