算子空间中秩一算子的稠密性

THE DENSITY OF RANK ONE OPERATORS IN OPERATORS SUBSPACES

设 M是 Hilbert空间上的σ-弱闭算子空间 ,称 M具有性质 (P) ,如果 M中秩一算子生成的子空间在 M中是 σ-弱稠密的 ;称 M具有扩张性质 (P) ,如果 M以及包含 M的每个 σ-弱闭子空间都具有性质 (P) .本文研究了性质 (P)和扩张性质 (P) 。

Let Mbe a operator subspace acting on a Hilbertspace,Mis said to have Property(P) ifthe subspace linearly generated by all rank one operators in Misσ-weakly dense in M,and to have extension property (P) if everyσ-weakly closed subspace including Mhas property (P) . The paper investigates property (P) and extension property(P) ,and gives a necessary and sufficientcondition fora operatorsubspace to have property(P) or extension property(P) respectively.