Title : ( Positive solutions of the system of operator equations $A_1X=C_1,XA_2=C_2, A_3XA^*_3=C_3, A_4XA^*_4=C_4$ in Hilbert $C^*$-modules )
Authors: R. Eskandari , X. Fang , Mohammad Sal Moslehian , Q. Xu ,
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Abstract
We give necessary and sufficient conditions for the operator system $A_1X=C_1, XA_2=C_2, A_3XA^*_3=C_3,$ and $ A_4XA^*_4=C_4$ to have a common positive solution, where $A_i$'s and $C_i$'s are adjointable operators on Hilbert $C^*$-modules. This corrects a published result by removing some gaps in its proof. Finally we give a technical example and show that our investigation in the setting of Hilbert $C^*$-modules is different from that of Hilbert spaces.
Keywords
, Hilbert $C^*$, module; Operator equation; Orthogonally complemented submodule
@article{paperid:1069247,
author = {R. Eskandari and X. Fang and Sal Moslehian, Mohammad and Q. Xu},
title = {Positive solutions of the system of operator equations $A_1X=C_1,XA_2=C_2, A_3XA^*_3=C_3, A_4XA^*_4=C_4$ in Hilbert $C^*$-modules},
journal = {Electronic Journal of Linear Algebra},
year = {2018},
volume = {34},
number = {1},
month = {August},
issn = {1537-9582},
pages = {381--388},
numpages = {7},
keywords = {Hilbert $C^*$-module; Operator equation; Orthogonally complemented submodule},
}
%0 Journal Article
%T Positive solutions of the system of operator equations $A_1X=C_1,XA_2=C_2, A_3XA^*_3=C_3, A_4XA^*_4=C_4$ in Hilbert $C^*$-modules
%A R. Eskandari
%A X. Fang
%A Sal Moslehian, Mohammad
%A Q. Xu
%J Electronic Journal of Linear Algebra
%@ 1537-9582
%D 2018
