Let $\phi: C(X,M_{4}(\mathbb{C})) \rightarrow C(Y,M_{8}(\mathbb{C})) $ be a $\ast$-homomorphism where $X$ and $Y$ are compact Hausdorff spaces. Let $M_{2}(\mathbb{C})$ be the C*-subalgebra of $C(X,M_{4}(\mathbb{C}))$. Can we conclude that $\phi(M_{2}(\mathbb{C}))$ is finite dimensional?
2026-03-30 03:52:42.1774842762
$\ast$-homomorphism
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