Definition:Annihilator of Subspace of Banach Space

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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:

$M^\bot = \set {g \in X^\ast : \map g x = 0 \text { for all } x \in M}$


Also see

  • Results about annihilators of subspaces of Banach spaces can be found here.


Sources