Approximate identity and approximation properties of multidimensional Fourier algebras

For a locally compact group $G$, let $A^n(G)$ denote the multidimensional Fourier algebra given by ${\otimes }_n^{eh}A(G)\mathrm{.}$ This work explores the approximation identity and operator amenability of the algebra $A^n(G)$. Further, we study the approximation properties (AP) and the concept of weak amenability of the multidimensional Fourier algebra.