The Open Mapping Theorem forces both pullback norms to be equivalent to the originals

Let X and Y be Banach spaces and $T:X\to Y$ be a bijective continuous linear map. If $\|\cdot\|_1$ and $\|\cdot\|_2$ denote the norms on X and Y respectively, define $\|x\|_3=\|Tx\|_2$ and $\|y\|_4=\|x\|_1$, where $Tx=y$, for all $x\in X$ and $y\in Y$. Then: