Example 41.11.11.label Let $S = \text{span}\bracsn{1, z, \ol z}\subset C(\mathbb{T})$, then $C^{*}(S) = C(\mathbb{T})$, but $S$ also embeds into and generates $C(\mathbb{D})$. In this particular case, $C(\mathbb{T}) = C^{*}_{\min}(S)$.
Example 41.11.11.label Let $S = \text{span}\bracsn{1, z, \ol z}\subset C(\mathbb{T})$, then $C^{*}(S) = C(\mathbb{T})$, but $S$ also embeds into and generates $C(\mathbb{D})$. In this particular case, $C(\mathbb{T}) = C^{*}_{\min}(S)$.
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