Timeline for Need reference for $\phi(Z)=Z'$ if and only if $\Phi: \operatorname{Prim}(Z')\to \operatorname{Prim}(Z)$ is injective
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| Jul 31, 2020 at 19:07 | comment | added | Douglas Somerset | I am not sure that I did, but Vesterstrom has it, so I felt safer with that hypothesis. In the non-unital case, the Stone-Weierstrass theorem requires "separates the points and vanishes nowhere", if I remember, so perhaps I did use it in line 2 of the second para. | |
| Jul 31, 2020 at 18:06 | comment | added | Math Lover | Sorry where did you use the fact that $A$ and $B$ are unital $C^{\ast}-$ algebras? | |
| Jul 31, 2020 at 13:03 | history | answered | Douglas Somerset | CC BY-SA 4.0 |