Category:Weakly Convergent Sequence in Normed Dual Space is Weakly-* Convergent
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This category contains pages concerning Weakly Convergent Sequence in Normed Dual Space is Weakly-* Convergent:
Let $\mathbb F$ be a subfield of $\C$.
Let $\struct {X, \norm {\, \cdot \,}_X}$ be a normed vector space over $\mathbb F$.
Let $\struct {X^\ast, \norm {\, \cdot \,}_{X^\ast} }$ be the normed dual space of $\struct {X, \norm {\, \cdot \,}_X}$.
Let $f \in X^\ast$.
Let $\sequence {f_n}_{n \mathop \in \N}$ be a sequence in $X^\ast$ converging weakly to $f$.
Then $\sequence {f_n}_{n \mathop \in \N}$ converges weakly-$\ast$ to $f$.
Pages in category "Weakly Convergent Sequence in Normed Dual Space is Weakly-* Convergent"
The following 3 pages are in this category, out of 3 total.