Tensor product of dual spaces and dual space of tensor product

Question

Let $\mathcal{A}$ and $\mathcal{B}$ be infinite-dimensional C*-algebras, and let $\mathcal{A}^*$ and $\mathcal{B}^*$ denote the space of norm-continuous linear functionals on $\mathcal{A}$ and $\mathcal{B}$, respectively. If $\gamma$ is the injective cross norm on the tensor product $\mathcal{A}\otimes\mathcal{B}$, and $\gamma^{*}$ is the adjoint cross norm of $\gamma$, is there any relation between $\mathcal{A}^{*}\otimes_{\gamma^{*}}\mathcal{B}^{*}$ and $(\mathcal{A}\otimes_{\gamma}\mathcal{B})^{*}$?