DOI QR코드

DOI QR Code

WEAK PROPERTY (βκ)

  • Cho, Kyugeun (Bangmok College of General Education Myong Ji University) ;
  • Lee, Chongsung (Department of Mathematics education Inha University)
  • Received : 2012.08.31
  • Accepted : 2012.10.10
  • Published : 2012.12.30

Abstract

In this paper, we define the weak property (${\beta}_{\kappa}$) and get the following strict implications. $$(UC){\Rightarrow}w-({\beta}_1){\Rightarrow}w-({\beta}_2){\Rightarrow}\;{\cdots}\;{\Rightarrow}w-({\beta}_{\infty}){\Rightarrow}(BS)$$.

Keywords

References

  1. K.G. Cho and C.S. Lee, Alternate signs ($A_k$) property in Banach spaces, Korean J. Math. 19 (2011), 301-308. https://doi.org/10.11568/kjm.2011.19.3.301
  2. Y. Cui, H. Hudzik and R. P luciennik, Weak orthogonality and weak property ($\beta$) in some Banach sequence spaces, Czechoslovak Math. J. 49 (1999), 303-316.
  3. S. Kakutani, Weak convergence in uniformly convex spaces, Tohoku Math. J. 45 (1938), 347-354.
  4. T. Nishiura and D. Waterman, Reflexivity and summability, Studia Math. 23 (1963), 53-57. https://doi.org/10.4064/sm-23-1-53-57
  5. J.R. Partington, On the Banach-Saks property, Math. Proc. Cambridge Philos. Soc. 82 (1977), 369-374. https://doi.org/10.1017/S0305004100054025

Cited by

  1. SOME UNIFORM GEOMETRICAL PROPERTIES IN BANACH SPACES vol.52, pp.2, 2015, https://doi.org/10.4134/BKMS.2015.52.2.505
  2. A NOTE ON SOME UNIFORM GEOMETRICAL PROPERTIES IN BANACH SPACES vol.22, pp.3, 2012, https://doi.org/10.11568/kjm.2014.22.3.463