thank you looks beautiful!
Could you please look at this
\begin{equation*}
\begin{split}
Ker T
&={f\inL^{p}(\mathbb{R}):Tf=0 a.e. on (0,1)}
&={f\inL^{p}(\mathbb{R}): f(tan(\pi x-\frac{\pi}{2}))\cdot\Bigl(\frac{\pi}{\cos^2(\pi x-\frac{\pi}{2})}\Bigr)^{\frac{1}{p}}=0 a.e}
&={f\inL^{p}(\mathbb{R}): f(t)=0 a.e. on \mathbb{R}}=0
\end{split}
\end{equation*}
Same problem as shown in my last reply. Pay attention to the end of a line.
By the way, it would very kind if you use the »Code« button when posting code to tag it as such (as you can see in my posts). You can find the button right above the input window when composing or editing a message. It just keeps your post clear and legible. And please get used to always providing a minimal example to describe a problem.