align double map function

i need write this map with this align.

i've tried this but is wrong

   \begin{align*}\psi\colon A&\longrightarrow& B(D) \\T&\longmapsto&\hat{T} \\&&  \hat{T}\colon D     &\longrightarrow        \mathbb{C}   \\ S          &&&\longmapsto      \hat{T}(S)\end{align*}

thanks