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Let $\mathcal{U}$ be an filter over $\mathbb{N}$. Define

$$c_{\mathcal{U}} = \{{(x_n)\in \ell_\infty\colon \lim_{\mathcal{U}, n}x_n =0\}},$$ which is a C*-algebra. Is there an accessible topological description of the maximal ideal space of $c_{\mathcal{U}}$? At least for ultrafilters?

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