Additive mappings on C∗-algebras sub-preserving absolute values of products

被引：0
作者：
Ali Taghavi
机构：
[1] University of Mazandaran,Department of Mathematics, Faculty of Mathematical Sciences
来源：
Journal of Inequalities and Applications | / 2012卷
关键词：
-algebra; -linear; -antilinear; homomorphism; linear preserver problem; real rank zero;
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摘要：
Let A be a C∗-algebra of real rank zero and B be a C∗-algebra with unit I. It is shown that if ϕ:A⟶B is an additive mapping which satisfies |ϕ(A)ϕ(B)|≤ϕ(|AB|) for every A,B∈A+ and ϕ(A)=I for some A∈As with ∥A∥≤1, then the restriction of mapping ϕ to As is a Jordan homomorphism, where As denotes the set of all self-adjoint elements. We will also show that if ϕ is surjective preserving the product and an absolute value, then ϕ is a C-linear or C-antilinear ∗-homomorphism on A.
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