Definition:Adjoint (Norm Theory)

Definition
Let $X$ and $Y$ be normed vector spaces.

Let $A: X \to Y$ be a linear operator between $X$ and $Y$.

Let $A^*: Y^* \to X^*$ be the linear operator defined as:
 * $\forall x, y \in Y: \innerprod {A x} y = \innerprod x {A^* y}$

Then $A^*$ is the adjoint of $A$.

Also known as
$A^*$ is also known as the dual of $A$.