Maps on matrix algebras preserving idempotents

被引：23
|
作者：
Dolinar, G [1 ]
机构：
[1] Univ Ljubljana, Fac Elect Engn, SI-10000 Ljubljana, Slovenia
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2003年 / 371卷
关键词：
nonlinear preserver problem; idempotent;
D O I：
10.1016/S0024-3795(03)00463-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M-n be the algebra of all n x n complex matrices and P-n the set of all idempotents in M-n. Suppose phi : M-n --> M-n is a surjective map satisfying A - lambdaB is an element of P-n if and only if phi(A) - lambdaphi(B) is an element of P-n, A, B is an element of M-n, lambda is an element of C. Then either phi is of the form phi(A) = TAT(-1), A is an element of M-n, or phi is of the form phi(A) = TA(t)T(-1), A is an element of M-n, where T is an element of M-n is a nonsingular matrix. (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码：287 / 300
页数：14
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