Article
Keywords:
Asplund space; weakly uniformly rotund norms; James spaces
Summary:
We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.
References:
                        
[1] Deville R., Godefroy G., Zizler V.: 
Smoothness and Renormings in Banach Spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics 64 (1993). 
MR 1211634 | 
Zbl 0782.46019[2] Diestel J.: 
Geometry of Banach Spaces-Selected Topics. Lecture Notes 485, SpringerVerlag, 1975. 
MR 0461094 | 
Zbl 0466.46021[3] Hagler J.: 
A counterexample to several questions about Banach spaces. Studia Math. 60 (1977), 289-308. 
MR 0442651 | 
Zbl 0387.46015[4] James R.C.: 
A non-reflexive Banach space isometric with its second conjugate. Proc. Nat. Acad. Sci. USA 37 (1951), 174-177. 
MR 0044024[5] James R.C.: 
A separable somewhat reflexive space with nonseparable dual. Bull. Amer. Math. Soc. 80 (1974), 738-743. 
MR 0417763[6] Lindenstrauss J., Stegall C.: 
Examples of separable spaces which do not contain $\ell_1$ and whose duals are non-separable. Studia Math. 54 (1975), 81-105. 
MR 0390720 | 
Zbl 0324.46017[7] Lindenstrauss J., Tzafriri L.: 
Classical Banach Spaces I, Sequence Spaces. Springer-Verlag, 1977. 
MR 0500056 | 
Zbl 0362.46013[8] Pelczynski A.: 
On Banach spaces containing $L_1(\mu)$. Studia Math. 30 (1968), 231-246. 
MR 0232195[9] Singer I.: 
On the problem of non-smoothness of non-reflexive second conjugate spaces. Bull. Austral. Math. Soc. 12 (1975), 407-416. 
MR 0383049 | 
Zbl 0299.46017[10] Stegall C.: 
The Radon-Nikodym property in conjugate Banach spaces. ibid. 206 (1975), 213-223. 
MR 0374381 | 
Zbl 0318.46056