Let $T : X \to Y$ be a bounded operator between normed spaces. $i_X: X \to X^{**}$ means the canonical embedding in the double dual space
This answer uses the commutativity of the following diagram $\require{AMScd}$ \begin{CD} X @>i_X>>X^{**} \\ @VTVV @VVT^{**}V \\ Y @>>i_Y> Y^{**}, \end{CD}
I understand the fin-dim case. I would like to know is there any more checking needed in comparison with a finite-dimensional case?
Here the case of a finite dimension is treated
