对称矩阵空间上的保秩算子(英文)

Rank One Preservers on Symmetric Matrix Spaces

设Ｆ为域，Ｓｎ（Ｆ）为Ｆ上的对称矩阵空间，Ｌ：Ｓｎ（Ｆ）→Ｓ(ｎ１)（Ｆ）（ｎ≥ｎ１）为保秩１算子，证明了Ｌ为如下形式之一：(A)L(X)=aPXPSn(F),n=n1(B)L()X=f(X)E(11)(n),Sn(F),n≥n1其中,Ｆ为一线性函数。

Suppose F is a field with F>3, L: S_n(F) →S_(n1)(F)(n≥n1) is a rank one preserver. The authors prove that L has one of the following forms: (A) L(X)=aPXP,XS_n(F), n = n1, (B) L(X)=f(X)E_(11)^(n),XS(F), n≥ n1, where F, peL.(F), and f : S.(F)→ F is a linear function.