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


Sources