完全分配格代数中秩一子代数的弱稠密性和套代数的一个特征

The Weak Density of the Rank One Subalgebra in Completely Distributive Subspace Lattice Algebras and a Characterization of Nest Algebras

如果 Ａ是 Ｈｉｌｂｅｒｔ 空间上的完全分配格代数， 那么Ａ中秩一算子生成的子代数在 Ａ中弱稠密， 当且仅当，Ａ在迹尖算子空间中的一次和二次预零化子的弱闭包是自反的；如果Ａ是套代数，那么ＬａｔＡ是极大套，当且仅当，Ａ的包含Ａ－的每个弱闭子空间是自反的。

If A is a completely distributive subspace lattice algebra on a Hilbert space, then the rank one subalgebra of A is weak dense in A if and only if, the weak closures of the first and the second preannihilators of A in the space of all trace class operators are reflexive. If A is a nest algebra, then Lat, A , the nest of all invariant subspaces of A, is maximal if and only if, all of the weak closed subspaces of A containing A-are reflexive.