Additive mappings on \(C^*\)-algebras sub-preserving absolute values of products (Q379091)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Additive mappings on \(C^*\)-algebras sub-preserving absolute values of products |
scientific article; zbMATH DE number 6224192
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Additive mappings on \(C^*\)-algebras sub-preserving absolute values of products |
scientific article; zbMATH DE number 6224192 |
Statements
Additive mappings on \(C^*\)-algebras sub-preserving absolute values of products (English)
0 references
8 November 2013
0 references
Let \(A\) and \(B\) be unital \(C^*\)-algebras and let \(\varphi:A\to B\) be an additive map satisfying \(|\varphi(a)\varphi(b)|\leq \varphi(|ab|)\) for all positive \(a,b\in A\). It is shown that, if \(A\) is of real rank zero and if there exists \(a\in A\) such that \(a^* = a\), \(\|a\|\leq 1\), and \(\varphi(a)=1\), then \(\varphi\) acts as a Jordan homomorphism on self-adjoint elements. Some variations of this result are also proved.
0 references
\(C^*\)-algebra
0 references
absolute value
0 references
additive mapping
0 references
linear preserver problem
0 references
real rank zero
0 references
0 references
