Generalized parallel sum of adjointable operators on Hilbert C-modules
Generalized parallel sum of adjointable operators on Hilbert C-modules
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Hilbert C 模上可共轭算子的广义并行和
DOI：
10.1080/03081087.2020.1793881
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发表时间：
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通讯作者：
Zamani Ali
中科院分区：
文献类型：
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作者：
Fu Chunhong;Moslehian Mohammad Sal;Xu Qingxiang;Zamani Ali
我们在Hilbert-模上的可伴随算子集上引入了可处理算子对的概念以及广义并行和的概念。将关于矩阵和Hilbert空间算子的并行和的一些重要结果推广到广义并行和的情形。特别地，证明了一个关于平行和的分解定理，并在Hilbert-模的情况下构造了两个正算子的公共上界。还讨论了Hilbert-模上正算子的调和平均。
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-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-module case. The harmonic mean for positive operators on Hilbert-modules is also dealt with.