数学物理学报(英文版) ›› 1992, Vol. 12 ›› Issue (1): 89-97.
那啟元
Na Qiyuan
摘要: In this paper we introduce a new concept, called the Schauder basis determining property, which is strictly stronger than the concept of a countably determining property. This concept provides a new way to study the structure of Banach spaces, especially, the goometrical properties of Banach spaces. We show that many structural properties of Banach spaces are Schauder basis determining properties. These include the Banach-Saks property, the Asplund property, full convexity, the Kadec-Klee property, refiexity, some-what refiexity, property (A)-(E), the Schur property, and the Krein-Milman property. We also give a counterexample to show that the approximation property is not a Schauder basis determining property, but it is a countably determining property.