# MAPS PRESERVING η-PRODUCT A⁎B+ηBA⁎ ON C⁎-ALGEBRAS

• Darvish, Vahid (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran) ;
• Nazari, Haji Mohammad (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran) ;
• Rohi, Hamid (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran) ;
• Taghavi, Ali (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
• Published : 2017.05.01
• 42 17

#### Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^*$-algebras such that $\mathcal{A}$ is prime. In this paper, we investigate the additivity of maps ${\Phi}$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective and satisfy $${\Phi}(A^*B+{\eta}BA^*)={\Phi}(A)^*{\Phi}(B)+{\eta}{\Phi}(B){\Phi}(A)^*$$ for all $A,B{\in}\mathcal{A}$ where ${\eta}$ is a non-zero scalar such that ${\eta}{\neq}{\pm}1$. Moreover, if ${\Phi}(I)$ is a projection, then ${\Phi}$ is a ${\ast}$-isomorphism.

#### Keywords

maps preserving ${\eta}$-product;${\ast}$-isomorphism;prime $C^*$-algebras

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#### Cited by

1. Maps preserving triple product A∗B + BA∗ on ∗-algebras pp.1793-7183, 2018, https://doi.org/10.1142/S1793557119500384