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Banach spaces which are M-ideals in their bidual have property (u). (English) Zbl 0659.46014
We show that every Banach space which is an M-ideal in its bidual has the property (u) of Pelczynski. Several consequences are mentioned.
Reviewer: G.Godefroy

MSC:
46B10 Duality and reflexivity in normed linear and Banach spaces
46B20 Geometry and structure of normed linear spaces
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References:
[1] E. M. ALFSEN, E. G. EFFROS, Structure in real Banach spaces I, Ann. of Math., 96 (1972), 98-128. · Zbl 0248.46019
[2] E. BEHRENDS, M-structure and the Banach-stone theorem, Lecture Notes in Mathematics 736, Springer-Verlag (1977). · Zbl 0436.46013
[3] E. BEHRENDS, P. HARMAND, Banach spaces which are proper M-ideals, Studia Mathematica, 81 (1985), 159-169. · Zbl 0529.46015
[4] G. A. EDGAR, An ordering of Banach spaces, Pacific J. of Maths, 108, 1 (1983), 83-98. · Zbl 0533.46007
[5] G. GODEFROY, On Riesz subsets of abelian discrete groups, Israel J. of Maths, 61, 3 (1988), 301-331. · 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). · 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. · Zbl 0545.46009
[11] A. LIMA, M-ideals of compact operators in classical Banach spaces, Math. Scand., 44 (1979), 207-217. · Zbl 0407.46019
[12] J. LINDENSTRAUSS, L. TZAFRIRI, Classical Banach spaces, Vol. II, Springer-Verlag (1979). · Zbl 0403.46022
[13] F. LUST, Produits tensoriels projectifs d’espaces de Banach faiblement sequentiellement complets, Coll. Math., 36-2 (1976), 255-267. · 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. · 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
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