强自反算子代数中的一秩算子

Rank-one Operators in strongly Reflexive Operater Algebras

本文给出了强自反算子代数是由其一秩算子σ—弱生成的一些充分条件。特别地证明了对于Von Neumann代数,强自反性与一秩算子代数的σ—弱稠密性是一致的。

In this short paper we point out some sufficient conditions fors trongly reflexive algebras to be σ-weakly generated by its rank-one operators. Particularly, it is proved that for Von Neumann algebra the strong reflexivity is equivalent to the density of its rank-one operator algebra.