Korean J. Math. Vol. 22 No. 3 (2014) pp.463-469
DOI: https://doi.org/10.11568/kjm.2014.22.3.463

A note on some uniform geometrical properties in Banach spaces

Main Article Content

Kyugeun Cho
Chongsung Lee

Abstract

In this paper, we investigate relationship between superreflexivity and weak property $(\beta_k)$. Indeed, we get the following diagram.



Article Details

Supporting Agencies

This work was supported by the Inha University Research Grant

References

[1] B. Beauzamy, Introduction to Banach spaces and their geometry, Mathematics Studies, 68, Noth-Holland, Amsterdam, 1982. Google Scholar

[2] K.G. Cho and C.S. Lee, Weak property (βk), Korean J. Math. 20 (2012), 415– 422. Google Scholar

[3] K.G. Cho and C.S. Lee, Superreflexivity and property (Dk) in Banach spaces, J. Appl. Math. Inform. 29 (2011), 1001–1006. Google Scholar

[4] S. Kakutani, Weak convergence in uniformly convex spaces, Tˆohoku Math. J. 45 (1938), 347–354. Google Scholar

[5] T. Nishiura and D. Waterman, Reflexivity and summability, Studia Math. 23 (1963), 53–57. Google Scholar