Hilbert C~*-模上可共轭算子的并联和

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

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.