Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.04.24
  • Published : 2017.05.01
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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.

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