TY - JOUR
ID - 724
TI - Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Guan, Y.
AU - Wang, C.
AU - Hou, J.
AD - Department of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.
AD - Department of Mathematics, Taiyuan
University of Technology, Taiyuan 030024, P.R.
China.
Y1 - 2015
PY - 2015
VL - 41
IS - Issue 7 (Special Issue)
SP - 85
EP - 98
KW - C$^*$-algebras
KW - additive maps
KW - Jordan homomorphism
KW - *-homomorphism
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_724.html
L1 - http://bims.iranjournals.ir/article_724_15cc6b48cc93f3f328eb35b3ec30359a.pdf
ER -