Multiplicative mappings at some points on matrix algebras |
| |
Authors: | Jun Zhu Changping Xiong |
| |
Institution: | a Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, PR China b Enshi Technical College, Enshi 445000, PR China |
| |
Abstract: | Let Mn be the algebra of all n×n matrices, and let φ:Mn→Mn be a linear mapping. We say that φ is a multiplicative mapping at G if φ(ST)=φ(S)φ(T) for any S,T∈Mn with ST=G. Fix G∈Mn, we say that G is an all-multiplicative point if every multiplicative linear bijection φ at G with φ(In)=In is a multiplicative mapping in Mn, where In is the unit matrix in Mn. We mainly show in this paper the following two results: (1) If G∈Mn with detG=0, then G is an all-multiplicative point in Mn; (2) If φ is an multiplicative mapping at In, then there exists an invertible matrix P∈Mn such that either φ(S)=PSP-1 for any S∈Mn or φ(T)=PTtrP-1 for any T∈Mn. |
| |
Keywords: | 47L30 15A30 47B47 |
本文献已被 ScienceDirect 等数据库收录! |
|