Dual operator

Summary

The dual operator of a bounded operator $T \colon X \to Y$ between normed spaces is the operator $T' \colon Y' \to X'$ between the continuous dual spaces given by $T'(f) = f \circ T$. It is the analytic form of the dual map of linear algebra, also called the transpose or Banach space adjoint. Many properties of $T$, such as having closed or dense range, can be read off from $T'$.