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Suppose $A\otimes B$ is the minimal tensor product of two unital $C^*$ algebras $A$ and $B$. We know that the set of states, $\{\phi\otimes\psi|\phi\in S(A),\psi\in S(B) \}$ on $A\otimes B$ separates the points of $A\otimes B$. Here $S(A)$ and $S(B)$ are the state spaces of $A$ and $B$ respectively. My question isIs : is there any reference for us to cite this result? |
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Reference request: tensor products of states separate the points of tensor product of $C^*$-alagebrasSuppose $A\otimes B$ is the minimal tensor product of two unital $C^*$ algebras $A$ and $B$. We know that the set of states, $\{\phi\otimes\psi|\phi\in S(A),\psi\in S(B) \}$ on $A\otimes B$ separates the points of $A\otimes B$. Here $S(A)$ and $S(B)$ are the state spaces of $A$ and $B$ respectively. My question is Is there any reference for us to cite this result?
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