Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China.
Abstract
Let $\mathcal {A} $ and $\mathcal {B} $ be C$^*$-algebras. Assume that $\mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $\Phi:\mathcal{A} \to\mathcal{B}$ is an additive map preserving $|\cdot|^k$ for all normal elements; that is, $\Phi(|A|^k)=|\Phi(A)|^k $ for all normal elements $A\in\mathcal A$, $\Phi(I)$ is a projection, and there exists a positive number $c$ such that $\Phi(iI)\Phi(iI)^{*}\leq
c\Phi(I)\Phi(I)^{*}$, then $\Phi$ is the sum of a linear Jordan *-homomorphism and a conjugate-linear Jordan *-homomorphism. If, moreover, the map $\Phi$ commutes with $|.|^k$ on $\mathcal{A}$, then $\Phi$ is the sum of a linear *-homomorphism and a conjugate-linear *-homomorphism. In the case when $k \not=1$, the assumption $\Phi(I)$ being a projection can be deleted.
Guan, Y., Wang, C. & Hou, J. (2015). Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 85-98.
MLA
Guan, Y., Wang, C., & Hou, J. "Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements", Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 85-98.
HARVARD
Guan Y., Wang C., Hou J. (2015). 'Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 85-98.
CHICAGO
Y. Guan, C. Wang & J. Hou, "Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements," Bulletin of the Iranian Mathematical Society, 41 Issue 7 (Special Issue) (2015): 85-98,
VANCOUVER
Guan Y., Wang C., Hou J. Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements. BIMS. 2015;41(Issue 7 (Special Issue)):85-98.
