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fixed typo, added tag
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YCor
YCor
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$*$–homomorphsims $*$–homomorphisms of the center of $C^*$-algebras

Let $A$ and $B$ be $C^*$-algebras with cenerscenters $Z_A$ and $Z_B$. Suppose $\rho：A\rightarrow B$ is a surjective $*$- homomorphism. It is easy to check $\rho(Z_A)\subset Z(B)$.

I wonder how to assure that $\rho(Z_A) \neq Z(B)$?

If $rho$ is not surjective, what is the relationship between $\rho(Z_A)$ and $Z_B$?

$*$–homomorphsims of the center of $C^*$-algebras

Let $A$ and $B$ be $C^*$-algebras with ceners $Z_A$ and $Z_B$. Suppose $\rho：A\rightarrow B$ is a surjective $*$- homomorphism. It is easy to check $\rho(Z_A)\subset Z(B)$.

I wonder how to assure that $\rho(Z_A) \neq Z(B)$?

If $rho$ is not surjective, what is the relationship between $\rho(Z_A)$ and $Z_B$?

$*$–homomorphisms of the center of $C^*$-algebras

Let $A$ and $B$ be $C^*$-algebras with centers $Z_A$ and $Z_B$. Suppose $\rho：A\rightarrow B$ is a surjective $*$- homomorphism. It is easy to check $\rho(Z_A)\subset Z(B)$.

I wonder how to assure that $\rho(Z_A) \neq Z(B)$?

If $rho$ is not surjective, what is the relationship between $\rho(Z_A)$ and $Z_B$?

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math112358
math112358
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$*$–homomorphsims of the center of $C^*$-algebras

Let $A$ and $B$ be $C^*$-algebras with ceners $Z_A$ and $Z_B$. Suppose $\rho：A\rightarrow B$ is a surjective $*$- homomorphism. It is easy to check $\rho(Z_A)\subset Z(B)$.

I wonder how to assure that $\rho(Z_A) \neq Z(B)$?

If $rho$ is not surjective, what is the relationship between $\rho(Z_A)$ and $Z_B$?