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Let $1$\ell^p_n(\mathbb{C})$ to itself since $z\mapsto \overline{z}$ is an isometry of $\mathbb{C}$.

Question: What are all isometries from $\ell^p_n(\mathbb{C})$ to itself?

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    I have my doubts about your characterization, and in particular the fact that it doesn't depend on $p$. Take for example $T=\begin{bmatrix}\cos t & \sin t \\ -\sin t & \cos t\end{bmatrix}$: this is a norm-preserving surjection of $\ell^2_2(\mathbb{R})$, but I don't think it has the form you claim. And it is not an isometry for choices of $p$ other than 2.2012-01-14

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