# Center of Minimal Tensor Product of $C^{\ast}$-Algebras

Let $$A$$ and $$B$$ be $$C^{\ast}-$$Algebras. Assume that $$A \otimes B$$ denotes the minimal (spatial) tensor product. Is it true that $$Z(A \otimes B)= Z(A) \otimes Z(B)$$ where $$Z$$ is used for center.

Note that $$Z(A) \otimes Z(B)\subset Z(A \otimes B)$$. Also as $$Z(A) \otimes Z(B)$$ is $$*$$-subalgebra Of $$A \otimes B$$ so using injectivity of min the identity map extends uniquely to an $$*$$-isometric map say $$\theta: Z(A)\otimes Z(B) \to Z(A\otimes B)$$. We only need to show $$\theta$$ is surjective. Any ideas?