BSE-property of tensor product Banach algebras

Let $A$ and $B$ be commutative semisimple Banach algebras. In this paper, the $BSE$ and $BED$- property of tensor Banach algebra $A{\otimes }_{\gamma }B$ with respect to the Banach algebras $A$ and $B$ are assesed. In particular, $BSE$ and $BED$- structure of vector-valued group algebra $L_1(G,A)$ and $C^{\ast }$- algebra $C_0(X,A)$ characterized.