Goldstine theorem

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In functional analysis, a branch of mathematics, the Goldstine theorem, named after Herman Goldstine, expresses the fact that a Banach space is weak*-dense in its bidual space.

More precisely:

[edit] Statement

For a Banach space X the canonical imbedding jX(BX) of its unit ball into its bidual is weak*-dense in the unit ball B_{X^{\ast\ast}} of its bidual.

[edit] See also