Title : ( Generalized parallel sum of adjointable operators on Hilbert C*-modules )
Authors: Chunhong Fu , Mohammad Sal Moslehian , Qingxiang Xu , Ali Zamani ,
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Abstract
We introduce the notion of tractable pair of operators as well as that of the generalized parallel sum in the setting of adjointable operators on Hilbert $C^*$-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 $C^*$-module case. The harmonic mean for positive operators on Hilbert $C^*$-modules is also dealt with.
Keywords
, Hilbert $C^*$-module, polar decomposition, parallel sum, generalized parallel sum, harmonic mean
@article{paperid:1082225,
author = {Chunhong Fu and Sal Moslehian, Mohammad and Qingxiang Xu and Ali Zamani},
title = {Generalized parallel sum of adjointable operators on Hilbert C*-modules},
journal = {Linear and Multilinear Algebra},
year = {2020},
volume = {70},
number = {12},
month = {July},
issn = {0308-1087},
pages = {2278--2296},
numpages = {18},
keywords = {Hilbert $C^*$-module; polar decomposition; parallel sum; generalized parallel sum; harmonic mean},
}
%0 Journal Article
%T Generalized parallel sum of adjointable operators on Hilbert C*-modules
%A Chunhong Fu
%A Sal Moslehian, Mohammad
%A Qingxiang Xu
%A Ali Zamani
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2020
