Suppose, that $A$ is a $C$-algebra. It follows, according to Sakai's book, that double dual of $A$ is also $C$-algebra. I'm not quite sure if I understand the proof correctly. Author proves that $A^{**}=\pi(A)''$ where $\pi$ is universal representation showing first that the corresponding preduals coincide. But preduals ale only Banach spaces, so the question rises: how do we define multiplication and involution in the second dual of $A$? I've heard that can be done in natural way (not using the universal representation), using so called Goldstein theorem but I don't know what precisely this theorem states. If we follow this 'natural' procedure via Goldstein theorem and simultaneously use universal representation we get that double dual of $A$ and $\pi(A)''$ are isomorphic as BANACH SPACES-but is it true that they are isomorhic as $C$ * algebras (in general it seems that this need not to be true as $\ell^{\infty}$ and $L^{\infty}[0,1]$ are isomorhic as Banach spaces but not as $C$ * algebras).