正交投影算子序列积的相关性质
On the Related Properties of the Sequential Product of Orthogonal Projection Operators

本文以复可分Hilbert空间为研究背景，聚焦正交投影算子序列积的相关性质展开探究。记$\epsilon \left(H\right)$ 为该空间全体正压缩算子的集合，为全体正交投影算子的集合。对于$A\in \epsilon \left(H\right)$ ，$B\in \epsilon \left(H\right)$ ，定义$A°B=A^{\frac{1}{2}}B{A}^{\frac{1}{2}}$ 为$A$ 和$B$ 的序列积。研究借助空间分解的方法，推导并证明了正交投影算子序列积在幂运算、广义逆存在性等方面的核心定理。
This paper takes the complex separable Hilbert space as the research background and focuses on exploring the relevant properties of the sequential product of orthogonal projection operators. Let $\epsilon \left(H\right)$ denote the set of all positive contraction operators on this space, and denote the set of all orthogonal projection operators. For $A\in \epsilon \left(H\right)$ , $B\in \epsilon \left(H\right)$ , the sequential product of A and B is defined as $A°B=A^{\frac{1}{2}}B{A}^{\frac{1}{2}}$ . By means of the