What's an example of nonzero non unital homomorphism between unital associative algebras?If there any example in case of Banach algebras?
2026-04-01 07:17:23.1775027843
Example of non unital homomorphism of algebras
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Consider $\phi:\mathbb{C}\to M_2(\mathbb{C})$ given by $\phi(z)=\begin{pmatrix}z&0\\0&0\end{pmatrix}$. This is a $*$-homomorphism between $C^*$-algebras, but it is of course non-unital since $\phi(1)\neq I_{M_2}$.