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On the parallel addition and subtraction of operators on a Hilbert space
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-11-18 , DOI: 10.1080/03081087.2020.1849007
Shuaijie Wang 1 , Xiaoyi Tian 1 , Chunyuan Deng 1
Affiliation  

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 A : B = ( A + B ) , B = ( A : B ) ÷ A , ( A C ) ÷ ( B C ) = ( A ÷ B ) C , A ÷ B = ( P ( A B ) P ) , B = A : ( B ÷ A ) , ( C A ) : ( C B ) = C ( A : B ) 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.



中文翻译:

关于希尔伯特空间上算子的并行加减法

在本文中,我们扩展了并行加法的操作 一种 和平行减法 一种 ÷ 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 一种 = 一种 + = 一种 ÷ 一种 一种 C ÷ C = 一种 ÷ C 一种 ÷ = P 一种 - P = 一种 ÷ 一种 C 一种 C = C 一种 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。

更新日期:2020-11-19
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