PlanetMath: weak* convergence in normed linear space

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weak* convergence in normed linear space

(Definition)

$(x'_n)\subset X'$
a Banach space
$\exists x'\in X':\forall x\in X:\lim_{n\rightarrow \infty} x(x'_n)\equiv x'_n(x)=x'(x)$ .
If is reflexive, then weak* convergence is the same as weak convergence

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"weak* convergence in normed linear space" is owned by bwebste. [ full author list (4) | owner history (1) ]

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