| Maps Preserving Commutativity up to a Factor on Standard Operator Algebras |
| Received:October 21, 2012 Revised:July 07, 2013 |
| Key Words:
preservers standard operator algebras commutativity up to a factor.
|
| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.111101250) and Innovative Research Team, Department of Applied Mathematics, Shanxi University of Finance & Economics. |
|
| Hits: 2807 |
| Download times: 2605 |
| Abstract: |
| Let $X$, $Y$ be real or complex Banach spaces with dimension greater than 2 and ${\mathcal A}$, ${\mathcal B}$ be standard operator algebras on $X$ and $Y$, respectively. Let $\Phi:\mathcal A \rightarrow \mathcal B$ be a unital surjective map. In this paper, we characterize the map $\Phi$ on $\mathcal A$ which satisfies $(A-B)R=\xi R(A-B)\Leftrightarrow (\Phi(A)-\Phi(B))\Phi(R)=\xi\Phi(R)(\Phi(A)-\Phi(B))$ for $A,B,R\in \mathcal A$ and for some scalar $\xi$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.06.007 |
| View Full Text View/Add Comment |
