Category:Weak-* Convergence (Normed Vector Spaces)
This category contains results about weak-$\ast$ convergence in the context of Normed Vector Spaces.
Definitions specific to this category can be found in Definitions/Weak-* Convergence (Normed Vector Spaces).
Let $\Bbb F \in \set {\R, \C}$.
Let $\struct {X, \norm \cdot}$ be a normed vector space over $\Bbb F$.
Let $\sequence {f_n}_{n \mathop \in \N}$ be a sequence of bounded linear functionals on $X$.
Let $f : X \to \Bbb F$ be a bounded linear functional.
Then we say that $\sequence {f_n}_{n \mathop \in \N}$ converges weakly-$\ast$ (read as "weakly-star") if and only if:
- $\map {f_n} x \to \map f x$ for each $x \in X$.
We say that $f$ is a weak-$\ast$ limit of $\sequence {f_n}_{n \mathop \in \N}$.
We denote this:
- $f_n \weakstarconv f$
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Weak-* Convergence (Normed Vector Spaces)"
The following 4 pages are in this category, out of 4 total.