A note on a theorem of James

作者：Valdivia Manuel^*

来源：Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas, 2011, 105(1): 139-148.

DOI：10.1007/s13398-011-0011-0

• Separable Banach space
• Monotone shrinking basis

Let (e(n))(n=1)(infinity) be the unit basis of the Banach space c(0). In this paper we prove that, if X is a separable Banach space, there is a closed bounded absolutely convex subset B of c(0) which has the following properties: (1) e(j) is an element of B, j = 1, 2,...', and (e(n))(n=1)(infinity) is a monotone shrinking basis of (c(0))(B). (2) (c(0))(B) has a topological complement Z in ((c(0))(B))** which is weak*-closed and isometric to X*. (3) The projection from ((c(0))(B))** onto Z along (c(0))(B) has norm one.

• 出版日期2011