If we have a unital *-homomorphism $\displaystyle \varphi:M_2(\mathbb{C})\rightarrow M_2(\mathbb{C})$ show that is must be a *-automorphism.

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- Mar 21st 2011, 10:11 PMMauritzvdwormunital *-homomorphism
If we have a unital *-homomorphism $\displaystyle \varphi:M_2(\mathbb{C})\rightarrow M_2(\mathbb{C})$ show that is must be a *-automorphism.

- Mar 22nd 2011, 01:21 AMOpalg
- Mar 22nd 2011, 01:35 AMMauritzvdworm
Aha, I see. Since $\displaystyle M_2(\mathbb{C})$ is simple it only has two closed two sided ideals, 0 and itself.