Semisimple commutative Banach algebras have either a unique uniform norm or uncountably many, plus a largest weakly regular closed subalgebra and largest closed ideals with UUNP and SEP.
Kaniuth, A course in commutative Banach algebras, Graduate Texts in Mathematics 246, Springer (2009)
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On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras
Semisimple commutative Banach algebras have either a unique uniform norm or uncountably many, plus a largest weakly regular closed subalgebra and largest closed ideals with UUNP and SEP.