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

Hermann Pfitzner

Studia Mathematica (1993)

  • Volume: 104, Issue: 1, page 91-98
  • ISSN: 0039-3223

Abstract

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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 .

How to cite

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Pfitzner, Hermann. "L-summands in their biduals have Pełczyński's property (V*)." Studia Mathematica 104.1 (1993): 91-98. <http://eudml.org/doc/215961>.

@article{Pfitzner1993,
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 $l^1$.},
author = {Pfitzner, Hermann},
journal = {Studia Mathematica},
keywords = {Banach spaces which are -summable in their biduals; predual of any von Neumann algebra; Pełczyński’s property ; reflexive; weakly sequentially complete; complemented copies of },
language = {eng},
number = {1},
pages = {91-98},
title = {L-summands in their biduals have Pełczyński's property (V*)},
url = {http://eudml.org/doc/215961},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Pfitzner, Hermann
TI - L-summands in their biduals have Pełczyński's property (V*)
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 1
SP - 91
EP - 98
AB - 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 $l^1$.
LA - eng
KW - Banach spaces which are -summable in their biduals; predual of any von Neumann algebra; Pełczyński’s property ; reflexive; weakly sequentially complete; complemented copies of
UR - http://eudml.org/doc/215961
ER -

References

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  1. [1] J. Diestel, Sequences and Series in Banach Spaces, Springer, Berlin 1984. 
  2. [2] G. A. Edgar, An ordering for the Banach spaces, Pacific J. Math. 108 (1983), 83-98. Zbl0533.46007
  3. [3] G. Godefroy, Sous-espaces bien disposés de L 1 - applications, Trans. Amer. Math. Soc. 286 (1984), 227-249. Zbl0521.46012
  4. [4] 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. 
  5. [5] G. Godefroy et M. Talagrand, Nouvelles classes d'espaces de Banach à prédual unique, Séminaire d'Analyse Fonctionnelle de l'Ecole Polytechnique, 1980-81. 
  6. [6] P. Harmand, M-Ideale und die Einbettung eines Banachraumes in seinen Bidualraum, Dissertation, FU Berlin, 1983. 
  7. [7] P. Harmand, D. Werner, and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, monograph in preparation. Zbl0789.46011
  8. [8] W. Hensgen, Contributions to the geometry of vector-valued H ∞ and L 1 / H 0 1 spaces, Habilitationsschrift, Universität Regensburg, 1992. 
  9. [9] R. C. James, Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550. Zbl0132.08902
  10. [10] 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. Zbl0631.46020
  11. [11] 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. Zbl0631.46021
  12. [12] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin 1977. Zbl0362.46013
  13. [13] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin 1979. Zbl0403.46022
  14. [14] A. Pełczyński, On the isomorphism of the spaces m and M, Bull. Acad. Polon. Sci. 6 (1958), 695-696. Zbl0085.09406
  15. [15] M. Takesaki, Theory of Operator Algebras I, Springer, Berlin 1979. Zbl0436.46043
  16. [16] M. Talagrand, A new type of affine Borel functions, Math. Scand. 54 (1984), 183-188. Zbl0562.46005

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