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AVERAGING PROPERTY IN BANACH SPACES

Cho, Kyug-Eeun

  • Published : 2002.11.01

Abstract

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

Keywords

Banach-Saks property;convex block Banach-Saks property;reflexivity;uniformly convex

References

  1. Tohoku Math. J. v.45 Weak convergence in uniformly convex spaces S. Kakutani
  2. Proc. Amer. Math. Soc. v.49 An ergodic superproperty of Banach spaces defined by a class of matrices A. Brunel;H. Fong;L. Sucheston
  3. Studia Math. v.42 On reflexivity and summability A. Baernstein
  4. Bull. Acad. Polon. Sci. v.26 The dual of Baernstein's space and the Banach-Saks property C. J. Seifert
  5. Studia Math. v.23 Reflexivity and summability T. Nishiura;D. Waterman

Cited by

  1. Asymptotic domination of operators on Köthe function spaces and convergence of sequences vol.279, pp.15, 2006, https://doi.org/10.1002/mana.200410448