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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 $\eta\neq \pm1$. Moreover, if $\Phi(I)$ is a projection, then $\Phi$ is a $\ast$-isomorphism.
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참고문헌 (22)
참고문헌 신청
A. Taghavi / / Additivity of maps preserving products AP±PA? / Mathematica Slovaca
A. Taghavi / 2012 / Additive mapping on C?-algebras preserving absolute values / Linear Multi-linear Algebra 60 (1) : 33 ~ 38
C. Li / 2013 / Nonlinear mappings preserving product XY +Y X? on factor von Neumann algebras / Linear Algebra Appl 438 (5) : 2339 ~ 2345
C. R. Mires / 1970 / Lie isomorphisms of factors / Trans. Amer. Math. Soc 147 : 5 ~ 63
C. R. Mires / 1971 / Lie isomorphisms of operator algebras / Pacific J. Math 38 : 717 ~ 735
A. Taghavi / 2012 / Additive mapping on C?-algebras preserving absolute values / Linear Multi-linear Algebra 60 (1) : 33 ~ 38
C. Li / 2013 / Nonlinear mappings preserving product XY +Y X? on factor von Neumann algebras / Linear Algebra Appl 438 (5) : 2339 ~ 2345
C. R. Mires / 1970 / Lie isomorphisms of factors / Trans. Amer. Math. Soc 147 : 5 ~ 63
C. R. Mires / 1971 / Lie isomorphisms of operator algebras / Pacific J. Math 38 : 717 ~ 735
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