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

• Results about dual operators can be found here.

Sources

• 2001: Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalucía, Jan Pelant and Václav Zizler: Functional Analysis and Infinite-Dimensional Geometry ... (previous) ... (next): Definition $2.27$