Banach-Krein-Šmulian theorem

Let E be a Banach spaceMathworldPlanetmath. A convex subset C of the dual spaceMathworldPlanetmath E* is closed in the weak-* topologyMathworldPlanetmath if and only if the intersectionMathworldPlanetmath of C with the ball Br(0) is weak-* closed for every r>0.


  • 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