矩阵代数上的可乘保持映射

Acta mathematica scientia,Series A ›› 2008, Vol. 28 ›› Issue (6): 1194-1205.

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Multiplication-Preserving Maps On Matrix Algebras

An Guimei|Hou Jinchuan

(Department of Mathematics, Shanxi Teachers University, Shanxi Linfen 041004)

Received:2006-10-10 Revised:2008-06-08 Online:2008-12-25 Published:2008-12-25
Contact: An Guimei

Abstract

Abstract:

In this paper, we give some structure features of the multiplicative maps and the rank preserving multiplicative maps on matrix algebra M_n(F), where F is a field. By applying these results, we get some characterizations of the multiplicative maps on complex matrix algebras which preserve any one of the spectral radius, numerical radius, numerical range, positivity, self-adjointness, normality and unitarity of matrices.

Key words: Multiplicative maps, Rank, Spectral radius, Normal matrices

CLC Number:

15A03

An Guimei|Hou Jinchuan. Multiplication-Preserving Maps On Matrix Algebras[J].Acta mathematica scientia,Series A, 2008, 28(6): 1194-1205.

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Multiplication-Preserving Maps On Matrix Algebras

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