IJPAM: Volume 25, No. 3 (2005)


Yongjin Li
Department of Mathematics
Sun Yat-sen University
Guangzhou, 510275, P.R. CHINA
e-mail: stslyj@zsu.edu.cn

Abstract.We prove that a Banach space $X$ has the Radon-Nikodým property if and only if for any equivalent norm $\Vert.\Vert _2$ on $X$, there exists an equivalent norm $\Vert.\Vert _1$ with $B_{(X, \Vert.\Vert _1)} \subseteq B_{(X, \Vert.\Vert _2) } \subseteq
r B_{(X, \Vert.\Vert _1)}$ for some $r > 0$, such that $B_{(X, \Vert.\Vert _1)}$ has a LUR point. A characterization of LUR point is also given.

Received: October 20, 2005

AMS Subject Classification: 46B20, 46B22

Key Words and Phrases: Radon-Nikodým property, LUR point, Rotund point, Krein-Milman property

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 3