Definition:Annihilator of Subspace of Banach Space

Definition
Let $X$ be a Banach space.

Let $M$ be a vector subspace of $X$.

Let $X^\ast$ be the normed dual space of $X$.

We define the annihilator $M^\bot$ by:


 * $M^\bot = \set {g \in X^\ast : \map g x \text { for all } x \in M}$

Also see

 * Annihilator of Subspace of Banach Space is Subspace of Normed Dual
 * Annihilator of Subspace of Banach Space is Weak-* Closed
 * Definition:Annihilator of Subspace of Normed Dual Space