PlanetMath: Banach-Krein-Šmulian theorem

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Banach-Krein-Šmulian theorem

(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 $B_{r}(0)$ is weak- closed for every .

Bibliography

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

"Banach-Krein-Šmulian theorem" is owned by georgiosl. [ full author list (2) | owner history (3) ]

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Keywords:

Banach space, convex set, weak-* topology

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Cross-references: ball, intersection, topology, closed, dual space, convex subset, Banach space

This is version 18 of Banach-Krein-Šmulian theorem, born on 2005-05-08, modified 2005-07-05.
Object id is 7026, canonical name is BanachKreinSmulianTheorem.
Accessed 1968 times total.

Classification:

46H05 (Functional analysis :: Topological algebras, normed rings and algebras, Banach algebras :: General theory of topological algebras)

Pending Errata and Addenda

None.[ View all 4 ]

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