对称算子空间上保持Jordan三重零积的映射

设H表示无限维复Hilbert空间，ε={eλ｜λ∈∧}是H的一组标准正交基，φy（H）表示H上关于ε的对称算予全体．研究了对称算子空间上保持Jordan三重零积的映射，若φ是φ（H）上的可加满射，则φ双边保持Jordan三重零积当且仅当存在非零常数c以及形上的有H线性或有界共轭线性可逆算子A满足AA^T=I，使得φ（T）=cATA^T，∨T∈φ（H）．

Maps preserving zero triple Jordan products on the space of symmetric operators

Let H be an infinite-dimensional complex Hilbert space and ε={eλ｜λ∈∧} be an orthogonal basis of H. Let φy（H） be the algebra of all symmetric operators on H with respect to ε. In this paper,the additive maps on φy（H） which preserving zero triple Jordan products in both directions are studied. It is shown that an additive surjection φ on φy（H） preserving zero triple Jordan products in both directions if and only if there exist a nonzero scalar c and a bounded linear or bounded conjugate linear invertible operator A satisfying AA^T=I such that φ（T）=cATA^T for all T∈φ（H）.