Definition:Dual Operator

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

Let $T : X \to Y$ be a bounded linear transformation.

Let $X^\ast$ and $Y^\ast$ be the normed duals of $X$ and $Y$ respectively.

We define the dual operator $T^\ast : Y^\ast \to X^\ast$ by:


 * $T^\ast f = f \circ T$

for each $f \in X^\ast$.

Also see

 * Dual Operator is Bounded Linear Transformation


 * Definition:Adjoint Linear Transformation