Banach spaces which are M -ideals in their bidual have property ( u )

Gilles Godefroy; D. Li

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 2, page 361-371
  • ISSN: 0373-0956

Abstract

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

How to cite

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Godefroy, Gilles, and Li, D.. "Banach spaces which are $M$-ideals in their bidual have property $(u)$." Annales de l'institut Fourier 39.2 (1989): 361-371. <http://eudml.org/doc/74834>.

@article{Godefroy1989,
abstract = {We show that every Banach space which is an $M$-ideal in its bidual has the property $(u)$ of Pelczynski. Several consequences are mentioned.},
author = {Godefroy, Gilles, Li, D.},
journal = {Annales de l'institut Fourier},
keywords = {M-ideal in its bidual; property (u) of Pelczynski},
language = {eng},
number = {2},
pages = {361-371},
publisher = {Association des Annales de l'Institut Fourier},
title = {Banach spaces which are $M$-ideals in their bidual have property $(u)$},
url = {http://eudml.org/doc/74834},
volume = {39},
year = {1989},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 2
SP - 361
EP - 371
AB - We show that every Banach space which is an $M$-ideal in its bidual has the property $(u)$ of Pelczynski. Several consequences are mentioned.
LA - eng
KW - M-ideal in its bidual; property (u) of Pelczynski
UR - http://eudml.org/doc/74834
ER -

References

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  2. [2] E. BEHRENDS, M-structure and the Banach-Stone theorem, Lecture Notes in Mathematics 736, Springer-Verlag (1977). Zbl0436.46013MR81b:46002
  3. [3] E. BEHRENDS, P. HARMAND, Banach spaces which are proper M-ideals, Studia Mathematica, 81 (1985), 159-169. Zbl0529.46015MR87f:46031
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  8. [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. Zbl0674.46010
  9. [9] G. GODEFROY, D. LI, Some natural families of M-ideals, to appear. Zbl0687.46010
  10. [10] P. HARMAND, A. LIMA, On spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc., 283-1 (1984), 253-264. Zbl0545.46009MR86b:46016
  11. [11] A. LIMA, M-ideals of compact operators in classical Banach spaces, Math. Scand., 44 (1979), 207-217. Zbl0407.46019MR81c:47047
  12. [12] J. LINDENSTRAUSS, L. TZAFRIRI, Classical Banach spaces, Vol. II, Springer-Verlag (1979). Zbl0403.46022MR81c:46001
  13. [13] F. LUST, Produits tensoriels projectifs d'espaces de Banach faiblement sequentiellement complets, Coll. Math., 36-2 (1976), 255-267. Zbl0356.46058MR55 #11072
  14. [14] A. PELCZYNSKI, Banach spaces on which every unconditionally convergent operator is weakly compact, Bull. Acad. Pol. Sciences, 10 (1962), 641-648. Zbl0107.32504MR26 #6785
  15. [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. Zbl0412.46042

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