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Let $T\in \text{Aut}(\ell^2(\mathbb{C}))$ and $T(x)=(a_1 x_1, a_2 x_2,\ldots)$ where $a=(a_i)_i \in \ell^\infty(\mathbb{C})$. How can I easily see what is $\sigma(T)$ and $\sigma_p(T)$ (that are the eigenvalues of $T$)?

Thanks.

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    To begin, not that the $a_i$ are eigenvalues of $T$.2012-11-14

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