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Yemon Choi
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Here are some scattered thoughts: I'm not sure if they really answer what you seem to be driving at.

Complex analysis still gives you examples with nasty maximal ideal spaces, e.g. $H^\infty(\Omega)$. Even when $\Omega$ is the open unit disc, the spectrum is non-metrizable and not at all straightforward to understand (there ought to be some discussion in Gamelin's book).

$L^\infty$ has non-metrizable spectrum, although its structure is in some sense not as mysterious as that of $H%\infty$.

Note that every Banach space $E$ embeds as a closed subspace of a uniform algebra. Namely, Take the canonical map from $E$ into $C(B)$, where $B$ is the closed unit ball of $E^*$ equipped with the weak$*$-topology, and let A be the closed subalgebra generated by the image of $E$.

Yemon Choi
  • 25.8k
  • 9
  • 69
  • 156