L-summands in their biduals have Pełczyński's property (V*)

Hermann Pfitzner

ArticleOriginal scientific text

Title

L-summands in their biduals have Pełczyński's property (V*)

Authors ¹

Affiliations

FB Mathematik, I. Institut, Arnimallee 3, D-1000 Berlin 33, Germany

Abstract

Banach spaces which are L-summands in their biduals - for example

l^{1}

, the predual of any von Neumann algebra, or the dual of the disc algebra - have Pełczyński's property (V*), which means that, roughly speaking, the space in question is either reflexive or is weakly sequentially complete and contains many complemented copies of

l^{1}

.

J. Diestel, Sequences and Series in Banach Spaces, Springer, Berlin 1984.
G. A. Edgar, An ordering for the Banach spaces, Pacific J. Math. 108 (1983), 83-98.
G. Godefroy, Sous-espaces bien disposés de $L^{1}$ - applications, Trans. Amer. Math. Soc. 286 (1984), 227-249.
G. Godefroy, Existence and uniqueness of isometric preduals: a survey, in: Bor-Luh Lin (ed.), Banach Space Theory, Proc. of the Iowa Workshop on Banach Space Theory 1987, Contemp. Math. 85, Amer. Math. Soc., 1989, 131-193.
G. Godefroy et M. Talagrand, Nouvelles classes d'espaces de Banach à prédual unique, Séminaire d'Analyse Fonctionnelle de l'Ecole Polytechnique, 1980-81.
P. Harmand, M-Ideale und die Einbettung eines Banachraumes in seinen Bidualraum, Dissertation, FU Berlin, 1983.
P. Harmand, D. Werner, and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, monograph in preparation.
W. Hensgen, Contributions to the geometry of vector-valued $H^{\infty}$ and $\frac{L^{1}}{H_{0}^{1}}$ spaces, Habilitationsschrift, Universität Regensburg, 1992.
R. C. James, Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550.
D. Li, Espaces L-facteurs de leurs biduaux: bonne disposition, meilleure approximation et propriété de Radon-Nikodym, Quart. J. Math. Oxford (2) 38 (1987), 229-243.
D. Li, Lifting properties for some quotients of $L^{1}$ -spaces and other spaces L-summand in their bidual, Math. Z. 199 (1988), 321-329.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin 1977.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin 1979.
A. Pełczyński, On the isomorphism of the spaces m and M, Bull. Acad. Polon. Sci. 6 (1958), 695-696.
M. Takesaki, Theory of Operator Algebras I, Springer, Berlin 1979.
M. Talagrand, A new type of affine Borel functions, Math. Scand. 54 (1984), 183-188.

Title

L-summands in their biduals have Pełczyński's property (V*)

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Abstract

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