Goldstine theorem
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In functional analysis, a branch of mathematics, the Goldstine theorem, named after Herman Goldstine, is stated as follows:
- Goldstine theorem. Let
be a Banach space, then the image of the closed unit ball
under the canonical embedding into the closed unit ball
of the bidual space
is a weak*-dense subset.
The conclusion of the theorem is not true for the norm topology, which can be seen by considering the Banach space of real sequences that converge to zero, c0 space and its bi-dual space Lp space