体上Hermitian矩阵空间保秩1的加法映射及其应用

Additive Rank 1 Preservers between Hermitian Matrix Space over Dimension Rings

命D表示带有对合的一个体,Hn(D)表示D上的n×nHermitian矩阵空间.本文刻画了某条件下从Hn(D)到Hm(D)保秩1的加法映射.作为应用,进一步刻画了Hn(D)上保一般线性群的加法映射.

Let D be a division ring which possesses an involution. Denote by Hn （D） the space of n x n Hermitian matrices over D . In this paper, the authors characterize the additive maps from Hn （D） into Hm （D） that preserve rank 1 in some addition. As an application, the additive maps that preserve the general linear group over H, （D） are further characterized.