Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME GEOMETRIC PROPERTY OF BANACH SPACES-PROPERTY (Ck)

  • Lee, Chongsung (Department of Mathematics education Inha University) ;
  • Cho, Kyugeun (Bangmok College of Basic Studies Myong Ji University)
  • Received : 2009.04.23
  • Published : 2009.06.30
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Abstract

In this paper, we define property ($C_k$) and show that Property ($C_k$) implies property ($C_{k+1}$). The converse does not hold. Moreover, we prove that property ($C_k$) implies the Banach-Saks property.

Keywords

References

  1. A. Baernstein, On reflexivity and summability, Studia Math. 42 (1972), 91-94. https://doi.org/10.4064/sm-42-1-91-94
  2. S. Banach and S. Saks, Sur convergence forte dans les champs Lp, Studia Math. 2 (1930), 51-57. https://doi.org/10.4064/sm-2-1-51-57
  3. J. Diestel, Geometry of Banach Spaces - Selected Topics, Springer-Verlag, Berlin, New York, 1975.
  4. J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York, 1984.
  5. S. Kakutani, Weak convergence in uniformly convex spaces, Tohoku Math. J. 45 (1938), 188-193.
  6. T. Nishiura and D. Waterman, Re°exivity and summability, Studia Math. 23 (1963), 53-57. https://doi.org/10.4064/sm-23-1-53-57
  7. J. Schreier, Ein Gegenbeispeil zur Theorie der schwachen Konvergenz, Studia Math. 2 (1930), 58-62. https://doi.org/10.4064/sm-2-1-58-62
  8. C. J. Seifert, The dual of Baernstein's space and the Banach-Saks property, Bull. Acad. Polon. Sci. 26 (1978), 237-239.