Let $\Omega$ be a compact Hausdorff space. Let us denote $B_{\infty}(\Omega)$ by the space of all bounded complex valued measurable functions. Let $A$ be an arbitrary Banach algebra and consider $B_{\infty}(\Omega,A)$, the space of all bounded $A$-valued measurable functions $f:\Omega\to A$.
Q. True or false: $B_{\infty}(\Omega,A)\simeq B_{\infty}(\Omega)\hat{\otimes} A$ ( up to isomorphism of Banach algebras).