在恒等算子处可乘的弱连续映射

Multiplicative Weak Continuous Mapping at Unit Operator

设H是复数域上的无限维Hilbert空间,φ是B(H)到自身弱连续的线性满射。得到了φ为自同构的充要条件是φ在恒等算子I处可乘。

Let H be an infinite dimensional complex Hilbert space and Φ be a surjective linear map on B（H）.It proved that if Φ is multiplicative at I and continuous in the weak operator topology then Φ is an spatial automorphism.