Banach-Krein-Šmulian theorem
Let be a Banach space. A convex subset of the dual
space
is closed in the weak- topology
if and only
if the intersection
of with the
ball is weak- closed for every .
References
- 1 Dunford, N., and J. T. Schwartz, Linear Operators, Part I, Interscience Publishers, 1967.
Title | Banach-Krein-Šmulian theorem |
---|---|
Canonical name | BanachKreinvSmulianTheorem |
Date of creation | 2013-03-22 15:14:52 |
Last modified on | 2013-03-22 15:14:52 |
Owner | georgiosl (7242) |
Last modified by | georgiosl (7242) |
Numerical id | 21 |
Author | georgiosl (7242) |
Entry type | Theorem |
Classification | msc 46H05 |