Suites de Cauchy faibles dans un espace de Banach - Applications. (French) Zbl 0556.46009
Sémin. de géométrie des esapces de Banach, Paris 1982, Publ. Math. Univ. Paris VII 16, 1-6 (1983).
[For the entire collection see Zbl 0547.00027.]
This paper is a short summary of the author’s article, Ann. Sci. Ec. Norm. Supér., IV. Ser. 16, 109-122 (1983; Zbl 0544.46011). In this article the relationship between the \(w^*\)-continuity of the isometries on several subsets of \(E^*\) and the uniqueness of preduals is investigated. In particular all the known results of uniqueness of the isometric predual are obtained by simple methods. On the other hand, some isometric conditions which ensure that a Banach space is weakly sequentially complete are given, this result has been intensively used by the author in Trans. Am. Math. Soc. 286, 227-249 (1984; Zbl 0521.46012).
This paper is a short summary of the author’s article, Ann. Sci. Ec. Norm. Supér., IV. Ser. 16, 109-122 (1983; Zbl 0544.46011). In this article the relationship between the \(w^*\)-continuity of the isometries on several subsets of \(E^*\) and the uniqueness of preduals is investigated. In particular all the known results of uniqueness of the isometric predual are obtained by simple methods. On the other hand, some isometric conditions which ensure that a Banach space is weakly sequentially complete are given, this result has been intensively used by the author in Trans. Am. Math. Soc. 286, 227-249 (1984; Zbl 0521.46012).
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
