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设是Hilbert空间上的σ-弱闭算子空间，称具有性质(P)，如果中秩一算子生成的子空间在中是σ-弱稠密的；称具有扩张性质(P)，如果以及包含的每个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)，给出了它们的等价描述.“,”Let be a operator subspace acting on a Hilbert space, is said tohave Property (P) if the subspace linearly generated by all rank one operators in is σ-weakly dense in ,and to have extension property (P) if every σ-weakly closed subspace including has property (P).The paper investigates property (P) and extension property (P),and gives a necessary and sufficient condition for a operator subspace to have property (P) or extension property (P) respectively.