In this paper, we extend the operations of parallel addition $A:B$ and parallel subtraction $A÷B$ from the cone of bounded nonnegative self-adjoint operators to the linear bounded operators on a Hilbert space. Some conditions for the relations $\begin{array}{rl}{A}^{†}:B^{†}& =(A+B{)}^{†},B=(A:B)÷A,(AC)÷(BC)=(A÷B)C,\\ A÷B& =\left(P\right(A^{†}-B^{†})P{)}^{†},B=A:(B÷A),(CA):(CB)=C(A:B)\end{array}$to be true are studied and the solution of the equation A:X = B is investigated. Moreover, some relationships between the parallel addition and subtraction of projections are obtained.

在本文中，我们扩展了并行加法的操作 $\mathrm{一种}：乙$ 和平行减法 $\mathrm{一种}÷乙$从有界非负自伴算子的锥到希尔伯特空间上的线性有界算子。关系的一些条件$\begin{array}{rl}{\mathrm{一种}}^{†}：{乙}^{†}& =（\mathrm{一种}+乙{）}^{†}，乙=（\mathrm{一种}：乙）÷\mathrm{一种}，（\mathrm{一种}C）÷（乙C）=（\mathrm{一种}÷乙）C，\\ \mathrm{一种}÷乙& =（P（{\mathrm{一种}}^{†}-{乙}^{†}）P{）}^{†}，乙=\mathrm{一种}：（乙÷\mathrm{一种}），（C\mathrm{一种}）：（C乙）=C（\mathrm{一种}：乙）\end{array}$研究为真的方程，并研究方程A的解：X  =  B。此外，获得了投影的平行加法和减法之间的一些关系。