[Tex/LaTex] Aligning definition of a function that maps into a function space


I'm writing a proof that the dual of l^p is l^q, and in that process, I define a function from l^q to (l^p)*. My current function definition looks like this:

  \varphi:\ell^q\longrightarrow (\ell^p)^*& \\
  \mathbf{x}\longmapsto f_{\mathbf{x}}:&\ell^p \longrightarrow\mathbb{C} \\
  &\mathbf{y}\longmapsto\sum_{k=1}^\infty x_k y_k

This produces the following result:

Typeset isomorphism

I would like to align the definition so that the arrows are directly above each other. I have tried to do this using alignment characters in the following manner:

  \varphi:\ell^q&\longrightarrow& (\ell^p)^*& \\
  \mathbf{x}&\longmapsto& f_{\mathbf{x}}:\ell^p &\longrightarrow&\mathbb{C} \\
  &&\mathbf{y}&\longmapsto&\sum_{k=1}^\infty x_k y_k

This gives the desired alignment, but mucks up the spacing:
enter image description here

I wonder if there's a way to typeset this so that the arrows are aligned, but no additional spacing is produced.

Best Answer

Use alignat*:

  \varphi:\ell^q&\longrightarrow& (\ell^p)^* \\
  \mathbf{x}&\longmapsto& f_{\mathbf{x}}:\ell^p &\longrightarrow\mathbb{C} \\
  &&\mathbf{y}&\longmapsto\sum_{k=1}^\infty x_k y_k

enter image description here

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