ArticleOriginal scientific text

Title

Some stability results for asymptotic norming properties of Banach spaces

Authors 1, 2

Affiliations

  1. Stat-Math Division, Indian Statistical Institute, 203, B. T. Road, Calcutta 700035, India
  2. Stat-Math Division, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

Keywords

c0- and l1-direct sum of Banach spaces, w-Asymptotic Norming Property, Hahn-Banach smoothness

Bibliography

  1. P. Bandyopadhyay and S. Basu, On a new asymptotic norming property, ISI Tech. Report No. 5/95, 1995.
  2. P. Bandyopadhyay and A. K. Roy, Some stability results for Banach spaces with the Mazur Intersection Property, Indag. Math. 1 (1990), 137-154.
  3. D. Chen and B. L. Lin, Ball separation properties in Banach spaces, preprint, 1995.
  4. D J. Diestel, Sequences and Series in Banach Spaces, Springer, Berlin, 1984.
  5. J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
  6. G. Godefroy, Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité, Israel J. Math. 38 (1981), 209-220.
  7. G. Godefroy, Applications à la dualité d'une propriété d'intersection de boules, Math. Z. 182 (1983), 233-236.
  8. P. Harmand, D. Werner and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, 1993.
  9. Z. Hu and B. L. Lin, On the asymptotic norming properties of Banach spaces, in: Proc. Conf. on Function Spaces (SIUE), Lecture Notes in Pure and Appl. Math. 136, Marcel Dekker, 1992, 195-210.
  10. Z. Hu and B. L. Lin, Smoothness and asymptotic norming properties in Banach spaces, Bull. Austral. Math. Soc. 45 (1992), 285-296.
  11. Z. Hu and B. L. Lin, RNP and CPCP in Lebesgue Bochner function spaces, Illinois J. Math. 37 (1993), 329-347.
  12. Z. Hu and M. A. Smith, On the extremal structure of the unit ball of the space C(K,X), in: Proc. Conf. on Function Spaces (SIUE), Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, 1995, 205-223.
  13. K N. J. Kalton, Spaces of compact operators, Math. Ann. 108 (1974), 267-278.
  14. L Å. Lima, Uniqueness of Hahn-Banach extensions and lifting of linear dependences, Math. Scand. 53 (1983), 97-113.
  15. Å. Lima, E. Oja, T. S. S. R. K. Rao and D. Werner, Geometry of operator spaces, Michigan Math. J. 41 (1994), 473-490.
  16. I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), 735-750.
  17. E. Oja and M. P oldvere, On subspaces of Banach spaces where every functional has a unique norm-preserving extension, Studia Math. 117 (1996), 289-306.
  18. P R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238-255.
  19. R T. S. S. R. K. Rao, Spaces with the Namioka-Phelps property have trivial L-structure, Arch. Math. (Basel) 62 (1994), 65-68.
  20. B. Sims and D. Yost, Linear Hahn-Banach extension operators, Proc. Edinburgh Math. Soc. 32 (1989), 53-57.
  21. S F. Sullivan, Geometrical properties determined by the higher duals of a Banach space, Illinois J. Math. 21 (1977), 315-331.
  22. Y D. Yost, Approximation by compact operators between C(X) spaces, J. Approx. Theory 49 (1987), 99-109.
Pages:
271-284
Main language of publication
English
Received
1996-05-24
Accepted
1997-05-20
Published
1998
Exact and natural sciences