Banach Journal of Mathematical Analysis

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

Fatmah B. Jamjoom, Antonio M. Peralta, and 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 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

Permanent link to this document
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

Subjects
Primary: 46L57: Derivations, dissipations and positive semigroups in C-algebras
Secondary: 47B47: Commutators, derivations, elementary operators, etc. 17B40: Automorphisms, derivations, other operators 46L70: Nonassociative selfadjoint operator algebras [See also 46H70, 46K70] 46L05: General theory of $C^*$-algebras 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22] 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

Keywords
(Jordan) weak amenability orthogonal form generalized derivation purely Jordan generalized derivation Lie Jordan derivation

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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