ABSTRACT

We introduce the notion of a tractable pair of operators as well as that of the generalized parallel sum in the setting of adjointable operators on Hilbert $C^{\ast }$-modules. Some significant results about the parallel sum known for matrices and Hilbert space operators are extended to the case of the generalized parallel sum. In particular, a factorization theorem on the parallel sum is proved, and a common upper bound of two positive operators is constructed in the Hilbert $C^{\ast }$-module case. The harmonic mean for positive operators on Hilbert $C^{\ast }$-modules is also dealt with.

中文翻译：

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Hilbert C*-modules 上可伴随算子的广义并行和

摘要

我们在希尔伯特的可邻接算子的设置中引入了可处理算子对的概念以及广义并行和的概念$C^{*}$-模块。关于矩阵和希尔伯特空间算子已知的并行和的一些重要结果被扩展到广义并行和的情况。特别地，证明了并行和的分解定理，并在希尔伯特中构造了两个正算子的公共上界。$C^{*}$-模块案例。Hilbert 上正算子的调和均值$C^{*}$-modules 也被处理。