Definition:Annihilator of Subspace of Normed Dual Space
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Definition
Let $X$ be a Banach space.
Let $X^\ast$ be the normed dual space of $X$.
Let $N$ be a vector subspace of $X^\ast$.
We define the annihilator ${}^\bot N$ by:
- ${}^\bot N = \set {x \in X : \map g x = 0 \text { for all } g \in N}$
Also see
- Annihilator of Subspace of Normed Dual Space is Subspace of Normed Dual
- Annihilator of Subspace of Normed Dual Space is Closed
- Definition:Annihilator of Subspace of Banach Space
Sources
- 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $4.6$: Annihilators