Recall that a ternary $C^*$-ring is a complex Banach space $X$, equipped with a associative ternary product $[.,.,.]:X^3 \to X$ which is linear in outer variables and conjugate linear in middle variable, $\|[a,a,a]\|= \|a\|^3$ and $$\|[a,b,c]\| \leq \| a \| \| b\|\| c\|$$

Is it known that second dual $X^{**}$ of ternary $C^*$-ring is again ternary $C^*$-ring?

Any references?