关于算子代数上强算子拓扑与弱算子拓扑的一点注记

A Note on the Strong Operator Topology and Weak Operator Topology in Operator Algebras

摘要: 设$\mathscr{H}$ 是复可分的Hilbert空间，是$\mathscr{H}$ 上所有正交投影构成的集合。中的投影不仅具有有界线性算子的线性运算、乘法运算以及*运算，中还有交与并运算。本文讨论了在某些条件下，投影族的交与并运算保持强算子拓扑(弱算子拓扑)的收敛性质。

Abstract: Let $\mathscr{H}$ be a complex Hilbert space, and be the set of all orthogonal projections in $ℬ\left(\mathscr{H}\right)$ . The projections in not only involve the linear operations, multiplication operations, and * operations of bounded linear operators, but also include the operations of meet and join within . This paper discusses the conditions under which the meet and join operations of projection families preserve strong operator topology (weak operator topology) convergence.