Geodesic
When is a Bi-Jordan Homomorphism Bi-homomorphism?
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 485 .

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For Banach algebras $\mathcal{A}$ and $\mathcal{B}$, we show that if $\mathcal{U}=\mathcal{A}×\mathcal{B}$ is commutative (weakly commutative), then each bi-Jordan homomorphism from $\mathcal{U}$ into a semisimple commutative Banach algebra $\mathcal{D}$ is a bi-homomorphism. We also prove the same result for 3-bi-Jordan homomorphism with the additional hypothesis that the Banach algebra $\mathcal{U}$ is unital.
Classification : 47B48 46L05, 46H25
Keywords: n-bi-homomorphism, n-bi-Jordan homomorphism, weakly commutative 
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     author = {A. Zivari-Kazempour},
     title = {When is a {Bi-Jordan} {Homomorphism} {Bi-homomorphism?}},
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A. Zivari-Kazempour. When is a Bi-Jordan Homomorphism Bi-homomorphism?. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 485 . http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a0/