Korean J. Math. Vol. 26 No. 1 (2018) pp.61-74
DOI: https://doi.org/10.11568/kjm.2018.26.1.61

Maps preserving Jordan triple product A∗B+BA∗ on ∗-algebras

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Published: Mar 30, 2018
Keywords:
Jordan triple product, ∗-isomorphism, Prime ∗-algebras
Mathematics Subject Classification:
47B48, 46L10

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Ali Taghavi
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.
Mojtaba Nouri
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.
Mehran Razeghi
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.
Vahid Darvish
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.

Abstract

Let A and B be two prime ∗-algebras. Let Φ:A→B be a bijective and satisfies Φ(A∙B∙A)=Φ(A)∙Φ(B)∙Φ(A), for all A,B∈A where A∙B=A∗B+BA∗. Then, Φ is additive. Moreover, if Φ(I) is idempotent then we show that Φ is R-linear ∗-isomorphism.


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