I have stuck on a problem on Linear operators... Could anybody help me?

I have a linear operator in a Hilbert Space $\displaystyle H=L^{2}(0,1)$ that is $\displaystyle Tf(x)=xf(1-x^{3})$ and I want to find $\displaystyle T^{*}$, $\displaystyle T^{*}T$ and $\displaystyle \left \| T \right \|$. What should I do?