## Banach Journal of Mathematical Analysis

### Jordan weak amenability and orthogonal forms on JB$^*$-algebras

#### 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 $\mathcal{J}^*$.

#### Article information

Source
Banach J. Math. Anal. Volume 9, Number 4 (2015), 126-145.

Dates
First available in Project Euclid: 17 April 2015

https://projecteuclid.org/euclid.bjma/1429286061

Digital Object Identifier
doi:10.15352/bjma/09-4-8

Mathematical Reviews number (MathSciNet)
MR3336887

Zentralblatt MATH identifier
06430467

#### Citation

Jamjoom, Fatmah B.; Peralta, Antonio M.; Siddiqui, Akhlaq A. Jordan weak amenability and orthogonal forms on JB$^*$-algebras. Banach J. Math. Anal. 9 (2015), no. 4, 126--145. doi:10.15352/bjma/09-4-8. https://projecteuclid.org/euclid.bjma/1429286061

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