additive maps on c$^*$-algebras commuting with $|.|^k$ on normal elements
نویسندگان
چکیده
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 $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a positive number $c$ such that $phi(ii)phi(ii)^{*}leq cphi(i)phi(i)^{*}$, 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.
منابع مشابه
Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements
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 $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...
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عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 41
شماره Issue 7 (Special Issue) 2015
کلمات کلیدی
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