Banach-Krein-Šmulian theorem
Let be a Banach space. A convex subset of the dualspace
is closed in the weak- topology
if and onlyif the intersection
of with theball is weak- closed for every .
References
- 1 Dunford, N., and J. T. Schwartz, Linear Operators,Part I, Interscience Publishers, 1967.