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

页码：287 / 300

页数：14

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