Hilbert C~*-模上可共轭算子的并联和  

The Parallel Sum for Adjointable Operators on Hilbert C~*-Modules

作　　者：罗未 宋传宁[1] 许庆祥[1] Wei LUO;Chuan Ning;SONG Qing(Department of Mathematics,Shanghai Normal University,Shanghai 200234,P.R.China)

机构地区：[1]上海师范大学数学系

出　　处：《数学学报（中文版）》2019年第4期541-552,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11671261);上海市科委基金资助项目(18590745200)

摘　　要：本文研究了Hilbert C^*-模上可共轭算子的并联和,推广了矩阵和Hilbert空间上有界线性算子的一些相关结果.通过举例说明:存在一个Hilbert C^*-模H,以及H上的两个可共轭的正算子A和B,使得算子方程A^1/2=(A+B)^1/2X, X∈L(H)无解,其中L(H)为H上的可共轭算子全体.The parallel sum for adjointable operators on Hilbert C^*-modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert C^*-modules. It is shown that there exist a Hilbert C^*-module H and two positive operators A, B ∈ L (H) such that the operator equation A1/2=(A + B)^1/2X, X ∈ L (H) has no solution, where L (H) denotes the set of all adjointable operators on H.

关 键 词：HILBERT C^*-模 MOORE-PENROSE逆 并联和 

分 类 号：O177.2[理学—数学]