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单词 BanachKreinvSmulianTheorem
释义

Banach-Krein-Šmulian theorem


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

References

  • 1 Dunford, N., and J. T. Schwartz, Linear Operators,Part I, Interscience Publishers, 1967.
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