保持算子乘积部分等距的可加映射

Additive maps preserving operator pairs whose products are partial isometries

设B(H)是复Hilbert空间H上的有界线性算子全体组成的Banach代数。证明B(H)上的可加满射Φ双边保持算子乘积是非零部分等距的充要条件是存在H上的酉算子或共轭酉算子U以及常数λ∈T,使得Φ(X)=λUXU~*,■X∈B(H),其中T表示复平面C上的单位圆周。同时,刻画了保持两个算子Jordan三乘积是非零部分等距的可加映射。

Let B （H） be the Banach algebra of all bounded linear operators on a complex space H. It is proved that an additive surjective map ucts of two operators in both directions, if on Ф （H） preserves nonzero partial isometries of prod and only if there is a unitary operator or anti-unitary operator U on H, such that Ф （X）=λUXU , V X∈B（H） for some constant λ with λ∈T, where T is the unit circle in the complex plane C. Moreover, characterizing additive surjective mappings pre serving Jordan triple products of two operators are also obtained.