Definition:Annihilator of Subspace of Normed Dual Space

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