对称算子空间上的保秩1线性映射(英文)

Rank one preserving linear maps on spaces of symmetric operators

设H是一个复Hilbert空间,S(H)为H上对称算子全体所成的集合,用Γ表示S(H)中秩1算子全体所成的集合.设L是S(H)上的映射,如果L(Γ)Γ,则称L是保秩1的.S(H)上保秩1的弱连续线性映射被刻画.

Let H be a complex Hilbert space, and let S（H） be the space of all symmetric operators on H. Denote by Г the subset of S（H） consisting of all rank one operators. A linear map L from S（H） to itself is called a rank one preserver on S（H） if L（Г） lohtain in F. A complete classification of all linear and weakly continuous rank one preservers on S（H） is given.