Previous |  Up |  Next

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
Partner of
EuDML logo