Abstract
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 Jordan 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 $\mathcal{J}^*$.
Citation
Fatmah B. Jamjoom. Antonio M. Peralta. Akhlaq A. Siddiqui. "Jordan weak amenability and orthogonal forms on JB$^*$-algebras." Banach J. Math. Anal. 9 (4) 126 - 145, 2015. https://doi.org/10.15352/bjma/09-4-8
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