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2015 Jordan weak amenability and orthogonal forms on JB$^*$-algebras
Fatmah B. Jamjoom, Antonio M. Peralta, Akhlaq A. Siddiqui
Banach J. Math. Anal. 9(4): 126-145 (2015). DOI: 10.15352/bjma/09-4-8

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 $\mathcal{J}^*$.

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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

Information

Published: 2015
First available in Project Euclid: 17 April 2015

zbMATH: 06430467
MathSciNet: MR3336887
Digital Object Identifier: 10.15352/bjma/09-4-8

Subjects:
Primary: 46L57
Secondary: 17B40, 43A25, 46L05, 46L70, 46L89, 47B47

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.9 • No. 4 • 2015
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