A bijective bounded linear map transported to a pair of isometric renormings

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