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arXiv · 1411.2712

Jordan weak amenability and orthogonal forms on JB*-algebras

Fatmah B. Jamjoom·Antonio M. Peralta·Akhlaq A. Siddiqui
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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 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 $\mathcal{J}^*$.

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Fatmah B. Jamjoom, Antonio M. Peralta, Akhlaq A. Siddiqui. 2014-11-11. Jordan weak amenability and orthogonal forms on JB*-algebras. https://arxiv.org/abs/1411.2712

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