We prove the existence of a linear isometric correspondence between the Banach space of all symmetric orthogonal forms on a JB$^*$-algebra $\mathcal{ J}$ and the Banach space of all purely Jordan generalized derivations from $\mathcal{ J}$ into $\mathcal{ J}^*$. We also establish the existence of a similar linear isometric correspondence between the Banach spaces of all anti-symmetric orthogonal forms on $\mathcal{ J}$, and of all Lie Jordan derivations from $\mathcal{ J}$ into $\mathcal{ J}^*$.
Categories: math.OA math.FA