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Jan 14, 2022 at 10:18 history edited Gabriel CC BY-SA 4.0
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Jan 14, 2022 at 10:17 comment added Gabriel @NameNo thank you for your remark, I hadn't realized that.
Jan 14, 2022 at 10:09 comment added NameNo Yes with purely real commutative C$^*$-algebras (involution is identity). But consider yourself what happens for general commutative real C$^*$-algebras (equivalently complex commutative C$^*$-algebras with a fixed involution), for example taking two copies of the same compact T$_2$ space and the involution, on the algebra of continuous functions, that corresponds to the exchange of the two components.
Jan 14, 2022 at 9:16 history edited Gabriel CC BY-SA 4.0
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Jan 14, 2022 at 9:03 history answered Gabriel CC BY-SA 4.0