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http://dx.doi.org/10.4134/BKMS.b180327

MAPS PRESERVING JORDAN AND ⁎-JORDAN TRIPLE PRODUCT ON OPERATOR ⁎-ALGEBRAS  

Darvish, Vahid (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Nouri, Mojtaba (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Razeghi, Mehran (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Taghavi, Ali (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 451-459 More about this Journal
Abstract
Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be two operator ${\ast}$-rings such that ${\mathcal{A}}$ is prime. In this paper, we show that if the map ${\Phi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves Jordan or ${\ast}$-Jordan triple product, then it is additive. Moreover, if ${\Phi}$ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of ${\Phi}$. Finally, we show that if ${\mathcal{A}}$ and ${\mathcal{B}}$ are two prime operator ${\ast}$-algebras, ${\Psi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves ${\ast}$-Jordan triple product, then ${\Psi}$ is a ${\mathbb{C}}$-linear or conjugate ${\mathbb{C}}$-linear ${\ast}$-isomorphism.
Keywords
${\ast}$-Jordan triple product; ${\ast}$-algebra;
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Times Cited By KSCI : 1  (Citation Analysis)
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